Dans ce travail, les équations moyennes des mouvements planétaires sont calculées à un ordre élevé grâce à une programmation en calcul formel dédié. Le système résultant comprend plus de 150 000 termes polynomiaux et fournit une très bonne approximation de l'évolution à long terme du système solaire. Le système d'équations est développé à ordre 2 dans les masses et l'ordre 5 en excentricité et inclinaison. le système de degré 3 est intégré analytiquement au premier ordre ce qui fournit une solution de plus de 25 000 termes. Le problème des petits diviseurs séculaires est discuté et une liste de petits diviseurs de grande amplitude dans la solution est donnée, le terme principal étant lié à l'argument $ g_1-g_5 + (s_2-s_1) $ qui intervient dans l'excentricité de Mercure et de Jupiter, et dans l'inclinaison de Mercure et de Vénus. Il est démontré que la présence de ces diviseurs compromet grandement la construction d'une solution analytique, sans tenir compte du fait que la même solution de degré 5 comprend plus de 3 000 000 termes. Les équations séculaires sont ensuite intégrées numériquement d'une façon très efficace sur plus de 1 million d'années, avec un pas de 500 ans pour toutes les planètes, après avoir rajouté la contribution moyenne de la relativité générale et de la Lune. Par comparaison avec les éphémérides DE102 sur plus de 3000 ans, il est démontré que les équations séculaires représentent très bien l'évolution à long terme du système solaire.

We investigate chaotic ionization of highly excited hydrogen atom in crossed electric and magnetic fields (Rydberg atom) and intra-molecular relaxation in planar carbonyl sulfide (OCS) molecule. The underlying theoretical framework of our studies is dynamical systems theory and periodic orbit theory. These theories offer formulae to compute expectation values of observables in chaotic systems with best accuracy available in given circumstances, however they require to have a good control and reliable numerical tools to compute unstable periodic orbits. We have developed such methods of computation and partitioning of the phase space of hydrogen atom in crossed at right angles electric and magnetic fields, represented by a two degree of freedom (dof) Hamiltonian system. We discuss extensions to a 3-dof setting by developing the methodology to compute unstable invariant tori, and applying it to the planar OCS, represented by a 3-dof Hamiltonian. We find such tori important in explaining anomalous relaxation rates in chemical reactions. Their potential application in Transition State Theory is discussed.

Les vésicules sont utilisées d'une manière extensive comme modèle pour comprendre les dynamiques et les déformations des globules rouges au niveau individuel, mais aussi concernant les phénomènes collectives et la rhéologie. La membrane de la vésicule résiste à la flexion mais pas au cisaillement, contrairement aux globules rouges, néanmoins elles partagent plusieurs propriétés dynamiques avec les globules rouges, comme le tank-treading (mouvement en chenille de char) et le tumbling (mouvement de bascule) sous écoulement de cisaillement, ou les formes parachutes et slippers (pantoufles) sous un écoulement de Poiseuille. Les globules rouges sont connus pour former des trains de cellules (clusters) dans la microcirculation attribués à la nature attractive des interactions hydrodynamiques. Nous avons étudié numériquement plusieurs types de problème comme:(i) les dynamiques de cellules isolées, (ii) le couplage hydrodynamique entre globules rouges (en utilisant les vésicules comme modèle) soumis à un écoulement de Poiseuille sous différent confinements; (iii) l'agrégation des globules rouges et la formation de rouleaux; et (iv) le rôle des macromolécules dans la formation de clusters sous écoulement. les résultats obtenus apportent un nouveau regard à la physique des objets déformables et sont transposables au cas de l'écoulement des globules rouges dans la microcirculation. / Vesicles are extensively used as a model for understanding dynamicsand deformation of red blood cells at the individual level but also regarding collective phenomena and rheology. Vesicles' membranes withstand to bending butdo not have a shear resistance, unlike red blood cells, but they still share several dynamical properties with red blood cells, like tank-treading and tumbling under linear shear flow, or parachute and slipper shapes under Poiseuille flow. The red blood cells are known to form train of cells in the microcirculation attributed to attractive hydrodynamic interactions. We investigate numerically several kind of problems such as: (i) the dynamics of isolated cells; (ii) the hydrodynamic coupling between the red blood cells (by using vesicles as a model) subject to a Poiseuille flow under different confinements; (iii) the aggregation of red blood cells and formation of rouleaux; and (iv) the contribution of macromolecules in the formation of clusters under flow condition. The obtained results give a new insight into thephysics of deformable objects under confinement that are transposable to the flow of red blood cells in the microcirculation.

La présente thèse décrit un projet de recherche multidisciplinaire qui porte sur la reconnaissance de l’émotion dans les sons, couvrant les théories psychologiques, l’analyse du signal acoustique,l’apprentissage automatique et la dynamique chaotique.Dans nos interactions et nos relations sociales, nous dépendons considérablement de la communication de l’information et de notre perception des messages transmis. En fait, la communication se produit lorsque les signaux transmettent des informations entre une source et une destination. Le signal peut être verbal, et l’information est ensuite portée par des motifs sonores, tels que des mots. Dans la communication vocale non verbale, cependant,l’information peut être des modèles perceptifs qui véhiculent des indices affectifs, que nous percevons et évaluons sous la forme d’intentions, d’attitudes, d’humeurs et d’émotions.La prévalence de la composante affective peut être observée dans les interactions informatiques humaines (HCI) où le développement d’applications automatisées qui comprennent et expriment les émotions est devenu crucial. De tels systèmes doivent être significatifs et faciles à utiliser pour l’utilisateur final, de sorte que notre interaction avec eux devient une expérience positive. Bien que la reconnaissance automatique des émotions dans les sons ait reçu une attention accrue au cours des dernières années, il s’agit encore d’un jeune domaine de recherche.Non seulement cela contribue à l’informatique affective en général, mais il fournit également une compréhension approfondie de la signification des sons dans notre vie quotidienne.Dans cette thèse, le problème de la reconnaissance des affects est abordé à partir d’une double perspective: nous commençons par adopter une approche standard de l’analyse acoustique du signal, où nous examinons et expérimentons les fonctionnalités existantes pour déterminer leur rôle dans la communication émotionnelle. Ensuite, nous nous tournons vers la dynamique chaotique et la symbolisation des séries temporelles, pour comprendre le rôle de la dynamique inhérente des sons dans l’expressivité affective. Nous menons nos études dans le contexte des sons non verbaux, à savoir les sons vocaux, musicaux et environnementaux.D’un point de vue de l’écoute humaine, une tâche d’annotation est menée pour construire un ground-truth de voix de chant non verbales, marquées par des descriptions catégoriques du modèle bidimensionnel d’émotions. Deux types de sons sont inclus dans l’étude: vocal et glottal.D’un point de vue psychologique, la présente recherche porte sur un débat qui existe depuis longtemps parmi les scientifiques et les psychologues, concernant les origines communes de la musique et de la voix. La question est abordée à partir d’une analyse acoustique ainsi que d’une approche dynamique non linéaire.D’un point de vue de la modélisation, ce travail propose une nouvelle approche dynamique non linéaire pour la reconnaissance de l’affect dans le son, basée sur la dynamique chaotique et la symbolisation adaptative des séries temporelles. Tout au long de cette thèse, les contrastes clés dans l’expressivité de l’émotion sont illustrés parmi les différents types de sons, à travers l’analyse des propriétés acoustiques, les métriques de la dynamique non linéaire et les performances des prédictions.Enfin, d’un point de vue progressif, nous suggérons que les travaux futurs étudient des caractéristiques motivées par les études cognitives. Nous suggérons également d’examiner dans quelle mesure nos caractéristiques reflètent les processus cognitifs. En outre, nous recommandons que nos fonctionnalités dynamiques soient testées dans des études à grande échelle de la reconnaissance d’émotions à travers la participation aux défis expérimentaux, dans le but de vérifier s’ils obtiennent un consensus. / The present thesis describes a multidisciplinary research project on emotion recognition in sounds, covering psychological theories, acoustic-based signal analysis, machine learning and chaotic dynamics.In our social interactions and relationships, we rely greatly on the communication of information and on our perception of the messages transmitted. In fact communication happens when signals transmit information between a source and a destination. The signal can be verbal,and the information is then carried by sound patterns, such as words. In non verbal vocal communication however, information can be perceptual patterns that convey affective cues,that we sense and appraise in the form of intentions, attitudes, moods and emotions.The prevalence of the affective component can be seen in human computer interactions(HCI) where the development of automated applications that understand and express emotions has become crucial. Such systems need to be meaningful and friendly to the end user, so thatour interaction with them becomes a positive experience. Although the automatic recognition of emotions in sounds has received increased attention in recent years, it is still a young fieldof research. Not only does it contribute to Affective Computing in general, but it also provides insight into the significance of sounds in our daily life.In this thesis the problem of affect recognition is addressed from a dual perspective: we start by taking a standard approach of acoustic-based signal analysis, where we survey and experiment with existing features to determine their role in emotion communication. Then,we turn to chaotic dynamics and time series symbolization, to understand the role of the inherent dynamics of sounds in affective expressiveness. We conduct our studies in the context of nonverbal sounds, namely voice, music and environmental sounds.From a human listening point of view, an annotation task is conducted to build a ground truth of nonverbal singing voices, labelled with categorical descriptions of the two-dimensional model of affect. Two types of sounds are included in the study: vocal and glottal.From a psychological perspective, the present research addresses a debate that is of long standing among scientists and psychologists, concerning the common origins of music and voice.The question is addressed from an acoustic-based analysis as well as a nonlinear dynamics approach.From a modeling viewpoint, this work proposes a novel nonlinear dynamics approach for the recognition of affect in sound, based on chaotic dynamics and adaptive time series symbolization.Throughout this thesis, key contrasts in the expressiveness of affect are illustrated among the different types of sounds, through the analysis of acoustic properties, nonlinear dynamics metrics and predictions performances. Finally from a progressive perspective, we suggest that future works investigate features that are motivated by cognitive studies. We also suggest to examine to what extent our features reflect cognitive processes. Additionally we recommend that our dynamic features be tested inlarge scale ER studies through the participation in ER challenges, with an aim to verify if they gain consensus.

Inicialmente, apresentam-se características de dispositivos eletrônicos conhecidos como PLLs (phase-locked loops). PLLs são amplamente empregados para se extrair sinais de tempo em canais de comunicação e em aplicações nas quais se deseja controle automático de freqüência. O objeto principal é estudar PLLs analógicos descritos por uma equação diferencial ordinária de terceira ordem. Assim, deduzem-se condições de estabilidade assintótica e identifica-se um regime de caos conservativo, que ocorre sob certas combinações de valores de parâmetros. Três métodos de controle não-linear/caótico são então apresentados e aplicados. Os métodos são os seguintes: o Método de Pyragas via realimentação de variável de estado; o Método de Pyragas com atraso temporal na realimentação; e o Método de Sinha, o qual efetua o controle perturbando um parâmetro do sistema. Simulações numéricas são levadas a cabo a fim de ilustrar o comportamento dinâmico do sistema quando sujeito à ação desses métodos. Este trabalho termina com um estudo de uma rede formada por uma cadeia de PLLs. Condições para soluções síncronas, periódicas e caóticas (dissipativas e conservativas) são deduzidas para tal rede. / Firstly, features of electronic devices known as PLLs (Phase-Locked Loops) are presented. PLLs are widely employed to extract time signals in communication channels and in applications where automatic control of frequency is desired. The main goal is to study analog PLLs described by a third-order nonlinear ordinary differential equation. Thus, conditions for asymptotic stability are derived and a regime of conservative chaos occurring under certain combinations of parameter values is identified. Then, three methods of control of nonlinear/ chaotic dynamics are presented and applied. The methods are the following: the Pyragas method via feedback of state variable; the Pyragas method with time delay in the feedback; and the Sinhas method, which performs the control by disturbing a parameter of the system. Numerical simulations are accomplished in order to illustrate the dynamical behavior of the system when subjected to the action of these methods. This work ends with a study of a single-chain PLL network. Conditions for synchronous, periodic and chaotic (dissipative and conservative) solutions are derived for such a network.

Nesta tese, uma família de memórias associativas bidirecionais caóticas (família C-BAM) é proposta, implementada e testada com o objetivo de estender a relevância da presença e do estudo do fenômeno caótico a modelos de redes associativas. Na modelagem da família C-BAM, todos os neurônios da memória associativa bidirecional caótica (BAM), BAM com atraso e BAM exponencial (eBAM) foram substituídos por neurônios caóticos. Cada parâmetro do neurônio caótico na família C-BAM tem sua influência estimada através do planejamento de experimentos, em diferentes dinâmicas. Com base no planejamento de experimentos, valores de parâmetros são selecionados a fim de ilustrar a emergência de comportamentos dinâmicos como bifurcação, caos determinístico e crise. A existência de dinâmicas caóticas é confirmada pelo cálculo dos expoentes de Lyapunov. Experimentos empíricos mostraram que a dinâmica caótica modifica a acessibilidade à memória da família C-BAM. Ao invés de recuperar um único par, como a família BAM fazia, a versão caótica é capaz de gerar uma grande diversidade de padrões recuperados, envolvendo complexas transições entre os padrões armazenados, para algumas variações paramétricas. Tal comportamento permite à família C-BAM acessar padrões inacessíveis às redes BAMs originais. Além disso, a nova acessibilidade à memória, na qual seqüências de recuperação (com diferentes tamanhos) compostas de padrões treinados e não treinados têm emergido, pode ser usada para modelar a habilidade de um indivíduo saltar passos na solução de uma tarefa. Esta tese seleciona a rede C-BAM para ilustrar que a seqüência de recuperação da rede pode modelar a habilidade de um noviço ou a habilidade de um especialista executar uma tarefa. Embora a família C-BAM possa alcançar todos os padrões armazenados durante o comportamento caótico, ela não consegue convergir para um padrão específico. Duas estratégias de controle são propostas para permitir que as redes caóticas convirjam para a memória desejada: o método de controle por pinagem e um método de controle adaptativo. Conseqüentemente, os modelos C-BAM podem, de fato, realizar a hetero-associação de memórias antes inacessíveis, e a rede C-BAM pode estabilizar-se no estado final de uma tarefa, dado o primeiro estado / In this thesis, a family of bidirectional associative memories (C-BAM family) is proposed, implemented and tested to extend the study of chaotic phenomenon in associative models. In the C-BAM model, all the original neurons of bidirectional associative memory (BAM), BAM with delay and exponenetial BAM (eBAM) were substituted for chaotic neurons. Based on the experimental design, values of C-BAM family parameters are set to illustrate the emergence of a diversity of dynamic behavior, such as bifurcation, deterministic chaos and crisis. The existence of the chaotic dynamics is confirmed by calculation of Lyapunov exponents. Empiric experiments showed that the chaotic dynamics modifies the behavior of memory accessibility. Instead of recalling a single pair, as BAM did, its chaotic version yielded a wide diversity of recalled patterns, involving complex transitions via memorized patterns for some parametric variations. Hence, C-BAM family can access patterns that original BAM family cannot. Moreover, the new way of memory accessibility, in which several recall sequences (with distinct sizes) composed of trained and nontrained patterns have emerged, can be used to model the ability of skipping steps by an individual in a task solution. This thesis selected C-BAM network to illustrate that the retrieval sequence can model the ability of a novice or the ability of an expert to execute a task. There are also illustrated cases in which a novice recall can be transformed into an expert recall through parametric variation. Although C-BAM family can reach all stored patterns during the chaotic behavior, it can not converge towards a specific pattern, consequently a desired output is not produced. In this thesis, two control strategies are proposed in order to make the chaotic networks to converge towards the desired memory: the pinning control method and the adaptive control method. Consequently, the C-BAM models can effectively realize the correct heteroassociation to former non-accessible memories and the C-BAM network can quickly be stabilized in the final state of a task, given the first state

A dinêmica caótica, em arranjos de bilhares eletrônicos bidimensionais e tridimensionais , em heteroestruturas semicondutoras de AlxGa1-xAs/GaAs foi estudada tanto de forma experimental como através de simulações numéricas. Como primeira parte, a dinâmica eletrônica caótica em super-redes de antipontos bidimensionais foi tratada sob a influência de campo magnético uniforme aplicado de forma pararela ao plano do gás de elétrons. Nestas circunstâncias, a anisotropia do contorno de Fermi do gás bidimensional de elétrons produzida pelo campo magnético pararelo, distorce fortemente a forma das trajetórias eletrônicas induzindo mudanças drásticas nas oscilações de comensurabilidade da magnetoresistência na região de campo fraco, em temperaturas criogênicas. Como segunda parte, arranjos de bilhares eletrônicos tridimensionais foram realizadas, pela primeira vez, através da gravação de super-redes retangulares de buracos mecânicos cilíndricos em poços quânticos parabólicos, os quais contêm o gás tridimensional de elétrons de alta mobilidade. Medidas de resistividade nestes sistemas revelam a presença de picos anomalos na região de campo fraco, em forma similar às medições em sistemas de antipontos bidimensionais. Foi calculada a dinâmica eletrônica do bilhar tridimensional analisando -se a evolução das trajetórias no espaço de fases através das seções espaciais de Poincaré. Calculou-se também a magnetoresistência pxx do gás tridimensional através da teoria de resposta linear, encontrando-se que a presença de ressonância não lineares é refletida nos picos anômalos observados. A realização destes sistemas permitiu o estudo de fenômenos físicos novos como as oscilações de comensurabilidade em sistemas tridimensionais e os efeitos de tamanho galvano-magnéticos devido às ressonâncias geométricas. / The chaotic electron dynamics in two-dimensional and three-dimensional arrays of elec­ tron billiards in ALx Ga1-xAs/GaAs semiconductor heterostructures has been studied in experimental way and also through numerical simulations. As a first part, the chaotic electron dynamics in two-dimensional antidot super-lattices has been studied under the influence of a uniform magnetic field applied in parallel configuration related to the plane of the electron gas. In this case, the Fermi contour anisotropy of the two-dimensional elec­ tron gas induced by the parallel field highly distorts the shape of the electron trajectories inducing pronounced changes in the commensurability peaks of the low field magnetoresis­ tance, in cryogenic temperatures. In the second part, arrays of three dimensional electron billiards were obtained, by first time, through the patterning of rectangular super-lattices of cylindrical voids in ALx Ga1-xAs/GaAs parabolic quantum wells containing a high mo­ bility three-dimensional electron gas. Resistivity measurements in these systems reveal anomalous peaks in the low magnetic field region in similar way as measurements in two-dimensional antidots systems. The electron dynamics of the three-dimensional bil­ liard was calculated, analyzing the evolution of trajectories in phase space by means of Poincaré space of sections. The magnetoresistance xx of the three-dimensional electron gas was calculated through linear responde theory, being found that nonlinear resonances are reflected in the observed anomalous peaks. The accomplishment os these systems allowed the study of new physical phenomena such as the commensurability oscillations in three-dimensional systems and size-effects due to geometrical resonances.

In this thesis, we have tried to explain the regular and irregular(chaotic) dynamics of worm like micellar solutions on applying shear, through a detailed study of the equation of motion of a nematic order parameter tensor coupled to a hydrodynamic velocity field. We have assumed spatial variations only along one direction i.e. the gradient direction(1D model). The resulting phase diagram shows various interesting steady states or phases such as spatiotemporal chaos, temporal and spatiotemporal periodicities, and alignment of the director axis along the imposed flow field. The coupling of the orientational degrees of freedom of the order parameter with the hydrodynamic flow field holds the key to the appearance of dynamic shear bands in the system. We have solved numerically a set of coupled nonlinear equations to obtain the order parameter stress developed in the system; the magnitude of the order parameter tensor, the biaxiality parameter and the orientation of the director axis of the nemato gens under shear have also been studied in detail. To study the phase diagram obtained by time integration of the equation of motion mathematically, a stability analysis of the fixed point of motion for various parameter values has been performed so that the location of the chaotic-to-aligned phase boundary is verified. Also in the periodic region of the phase diagram, the stability of limit cycles is tested by analysing the fixed point of the corresponding Poincare map. Stability analysis of the periodic orbits leads to the observation that in the parameter space, there are regions of phase coexistence where chaotic or spatiotemporally intermittent behaviour coexists with periodic behaviour. When corrections in the imposed velocity field due to the order parameter stress were taken into account and the order parameter response was looked into at several points in the parameter space, the modified equations of motion were found to reproduce the earlier behaviour in all the different regimes if the value of a dimensionless viscosity parameter is taken to be such that the bare viscous stress overrides the order parameter stress. The phase boundaries are however different from the ones seen in the earlier model. However, for a choice of the viscosity parameter such that the order parameter stress and the bare viscous stress are comparable, we see two distinctly different attractors: a banded, periodic one that is common to both α1equalto 0, and not equal to 0 and a banded chaotic one for α1not equal to 0. Here, α1is a parameter that governs the nonlinearity in the stretching of the order parameter tensor along the direction of the applied shear. Quantitative analysis of the various chaotic attractors throws up not only positive Lyapunov exponents but also that the banded chaos is a “flip-flop” kind of chaos where the switching between two long-lived states of high and lows hear stress is chaotic, where as the behaviour in either of the two states is periodic, with either a single, isolated frequency or a bunch of harmonics. Also, the spatial correlation of the shear stress in the chaotic attractors is of much larger range than the temporal correlation, the latter being almost delta-function-like. On increasing the temperature of the system till it is above the isotropic–nematic transition temperature in the absence of shear, we find that under shear, similar attractors as those in the nematic case are observed, both for passive advection and for the full 1D hydrodynamics. This is an encouraging result since actual experiments are performed at a temperature for which the system is in the isotropic phase in the absence of shear. Thus for the 1D system, the parameter space has been explored quite extensively. Considering spatial variations only along the gradient axis of the system under shear is not enough since experiments have observed interesting behaviour in the vorticity plane in which Taylor velocity rolls were noted. Hence taking the system to 2D was necessary. Our numerical study of the 2D system under shear is incomplete because we came across computational difficulties. However, on shorter time scales we have seen a two-banded state with an oscillating interface and Taylor velocity rolls as well. The methodology used for the 2D study can also be used to reproduce the 1D results by the simple step of taking initial condition with no variation in the vorticity direction. This automatically ensures that no variation in the vorticity direction ever builds up because the equations of motion ensure that these variations in the system do not grow by themselves unless fed in at the start. Using this method, we were able to reproduce all the attractors found in the 1D calculation. Thus the 1D attractors have been observed using two different methods of calculation. Further work on the full 2D numerics needs to be done because we believe that spatiotemporally complex steady-state attractor s exist in the 2D system also for appropriate values of the parameters.

A dinêmica caótica, em arranjos de bilhares eletrônicos bidimensionais e tridimensionais , em heteroestruturas semicondutoras de AlxGa1-xAs/GaAs foi estudada tanto de forma experimental como através de simulações numéricas. Como primeira parte, a dinâmica eletrônica caótica em super-redes de antipontos bidimensionais foi tratada sob a influência de campo magnético uniforme aplicado de forma pararela ao plano do gás de elétrons. Nestas circunstâncias, a anisotropia do contorno de Fermi do gás bidimensional de elétrons produzida pelo campo magnético pararelo, distorce fortemente a forma das trajetórias eletrônicas induzindo mudanças drásticas nas oscilações de comensurabilidade da magnetoresistência na região de campo fraco, em temperaturas criogênicas. Como segunda parte, arranjos de bilhares eletrônicos tridimensionais foram realizadas, pela primeira vez, através da gravação de super-redes retangulares de buracos mecânicos cilíndricos em poços quânticos parabólicos, os quais contêm o gás tridimensional de elétrons de alta mobilidade. Medidas de resistividade nestes sistemas revelam a presença de picos anomalos na região de campo fraco, em forma similar às medições em sistemas de antipontos bidimensionais. Foi calculada a dinâmica eletrônica do bilhar tridimensional analisando -se a evolução das trajetórias no espaço de fases através das seções espaciais de Poincaré. Calculou-se também a magnetoresistência pxx do gás tridimensional através da teoria de resposta linear, encontrando-se que a presença de ressonância não lineares é refletida nos picos anômalos observados. A realização destes sistemas permitiu o estudo de fenômenos físicos novos como as oscilações de comensurabilidade em sistemas tridimensionais e os efeitos de tamanho galvano-magnéticos devido às ressonâncias geométricas. / The chaotic electron dynamics in two-dimensional and three-dimensional arrays of elec­ tron billiards in ALx Ga1-xAs/GaAs semiconductor heterostructures has been studied in experimental way and also through numerical simulations. As a first part, the chaotic electron dynamics in two-dimensional antidot super-lattices has been studied under the influence of a uniform magnetic field applied in parallel configuration related to the plane of the electron gas. In this case, the Fermi contour anisotropy of the two-dimensional elec­ tron gas induced by the parallel field highly distorts the shape of the electron trajectories inducing pronounced changes in the commensurability peaks of the low field magnetoresis­ tance, in cryogenic temperatures. In the second part, arrays of three dimensional electron billiards were obtained, by first time, through the patterning of rectangular super-lattices of cylindrical voids in ALx Ga1-xAs/GaAs parabolic quantum wells containing a high mo­ bility three-dimensional electron gas. Resistivity measurements in these systems reveal anomalous peaks in the low magnetic field region in similar way as measurements in two-dimensional antidots systems. The electron dynamics of the three-dimensional bil­ liard was calculated, analyzing the evolution of trajectories in phase space by means of Poincaré space of sections. The magnetoresistance xx of the three-dimensional electron gas was calculated through linear responde theory, being found that nonlinear resonances are reflected in the observed anomalous peaks. The accomplishment os these systems allowed the study of new physical phenomena such as the commensurability oscillations in three-dimensional systems and size-effects due to geometrical resonances.

Le travail de recherche présenté dans ce manuscrit est une contribution à l'étude des transitoires d'attaque dans les instruments auto-oscillants de type clarinette. L'objectif principal est d'analyser le comportement de l'instrument en réponse à une variation lente et linéaire de la pression dans la bouche du musicien. Dans des simulations numériques ou des expériences in vitro, lorsque la pression dans la bouche du musicien varie lentement et linéairement dans le temps, on observe en général l'apparition du son lorsque la pression dans la bouche atteint une valeur, appelée seuil d'oscillation dynamique, supérieure au seuil d'oscillation statique théorique. L'apport principal de ce travail est d'interpréter ce phénomène par la présence d'un retard à la bifurcation. L'approche analytique est privilégiée. La contribution majeure de ce doctorat est de comprendre les fondements de la théorie de la bifurcation dynamique et de s'inspirer de la méthodologie pour étudier le retard à la bifurcation dans un modèle de clarinette simple et bien connu de (le modèle dit "de Raman"). Les propriétés du seuil dynamique d'oscillation sont ainsi reliées aux caractéristiques de la variation temporelle de la pression dans la bouche que sont sa valeur initiale et sa pente. L'une des caractéristiques notoires du retard à la bifurcation se révèle être sa grande dépendance au bruit, même si ce dernier provient des erreurs d'arrondi de l'ordinateur. Les propriétés du seuil dynamique changent selon que le bruit peut être ignoré ou non. Nous montrons ensuite expérimentalement à l'aide d'une bouche artificielle et d'une clarinette de laboratoire que le retard à la bifurcation n'est pas qu'un phénomène numérique. Il est ainsi non seulement mis en évidence expérimentalement, mais ses propriétés sont également étudiés et comparées avec celles obtenues dans le cas numérique.