Orientadores: José Raimundo de Oliveira, Ignacio Bravo Muñoz / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-21T12:37:43Z (GMT). No. of bitstreams: 1 Fazanaro_FilipeIeda_D.pdf: 53323687 bytes, checksum: 76694b226ed99a337ecee1769ed9c4e0 (MD5) Previous issue date: 2012 / Résumén: Esta tesis tiene como objetivo la caracterización de sistemas dinámicos no lineales y abruptos. Se propone una nueva metodología para la estimación del espectro de Lyapunov capaz de superar las dificultades relacionadas en los sistemas basados en funciones lineales por partes sobre la aplicación de los métodos clásicos de cálculo (cuando se utiliza linealización local o análisis de series de las series temporales experimentales). Este enfoque, denominado como Dinámica de los Clones, realiza la estimación del espectro de Lyapunov y también mejora el estudio de las características topológicas relacionadas con los procesos de mezcla que dan lugar al comportamiento caótico. Este estudio se lleva a cabo utilizando las Estructuras Coherentes de Lagrange que pueden obtenerse a través de la construcción de un campo de Exponentes de Lyapunov de Tiempo Finito donde se puede identificar a las crestas (o las separatrices) que dan la posibilidad de identificar las distintas regiones de convergencia y divergencia del espacio de estados. Debido al hecho que esta tesis se desarrolla fundamentalmente bajo un ordenador, los aspectos prácticos involucrados en los experimentos numéricos necesarios, emplean algunos conceptos y herramientas de computación en paralelo. Esto último permitió la optimización de los algoritmos implementados. Por lo tanto, los experimentos se realizaron para verificar la eficacia del enfoque de las Dinámicas Clonadas para la caracterización del circuito de Chua, y también para obtener las Estructuras Coherentes de Lagrange que tienen relación con los modelos dinámicos capaces de generar atractores caóticos multiscroll / Resumo: Essa tese objetiva caracterizar sistemas dinâmicos não lineares não suaves. Para tal, é proposta uma nova abordagem de estimação do espectro de Lyapunov capaz de contornar as dificuldades intrínsecas aos sistemas estruturados por funções lineares por partes quando da aplicação de metodologias clássicas (baseadas em linearizações locais ou em análises de séries temporais). Essa abordagem possibilita a estimação do espectro de Lyapunov e, além disso, auxilia no estudo das características topológicas relacionadas aos processos de mistura que dão origem ao comportamento caótico. Essa linha de estudo é realizada através das Estruturas Lagrangianas Coerentes, as quais são obtidas pela construção de um campo de Expoentes de Lyapunov de Tempo Finito, onde é possível identificar cristas (ou separatrizes) que dividem regiões de convergência e de divergência no espaço de estados. Por se tratar de um trabalho basicamente computacional, essa tese contempla os aspectos práticos envolvidos para a realização dos experimentos numéricos através da utilização de alguns conceitos e ferramentas de computação paralela, o que possibilitou a otimização dos algoritmos implementados. Nesse sentido, os experimentos foram realizados de modo a verificar a eficácia da metodologia proposta para a caracterização do circuito de Chua e, ainda, foram obtidas as Estruturas Lagrangianas Coerentes para os modelos dinâmicos capazes de gerar atratores caóticos multiscroll / Abstract: This thesis aims to characterize non-smooth nonlinear dynamical systems. To accomplish this purpose, we propose a new approach for estimating the Lyapunov spectrum which is capable to overcome the intrinsic difficulties of classical methods (based on local linearization or time series analysis) when dealing with systems based on piecewise linear functions. This approach, called Cloned Dynamics, allows the estimation of the Lyapunov spectrum and also improves the study of the topological features related to the mixing processes that give rise to the chaotic behavior. This study is performed using the Lagrangian Coherent Structures which are obtained by the construction of a Finite Time Lyapunov Exponents field where it is possible to identify the ridges (or the separatrices) which divide the convergence and divergence regions of the state space. Due to the fact that this thesis is basically developed under a computer environment, the practical features involved in the numerical experiments employing some parallel computing concepts and tools are discussed, which allowed the optimization of the algorithms implemented. In this sense, experiments were performed to verify the effectiveness of the Cloned Dynamics approach for the characterization of the Chua's circuit, and also to obtain the Lagrangian Coherent Structures related to the dynamical models capable of generating multiscroll chaotic attractors / Doutorado / Automação / Doutor em Engenharia Elétrica

Les travaux de thèse sont consacrés à l’étude numérique de l’application de macro-déformations successives alternées a la paroi d’un tube. La modification de l’écoulement du fait des déformations permet de modifier ses propriétés en termes de transfert thermique et de mélange. L’objectif de l’étude d’un tel dispositif est entre autre de l’appliquer pour des configurations d’échangeurs multifonctionnels, qui sont à la fois échangeurs de chaleur et réacteurs chimiques. L’étude s’intéresse principalement aux écoulements laminaires. Les calculs sont réalisés avec le code ANSYS Fluent. L’étude est tout d’abord consacrée à la caractérisation de l’écoulement secondaire créé par les déformations ainsi qu’à l’influence des différents paramètres de déformation. Afin d’améliorer le mélange dans l’écoulement, l’étude d’une configuration coaxiale déformée a été envisagée (cette géométrie correspond de plus à une configuration d’écoulement utilisée dans l’industrie). Deux configurations annulaires ont été considérées. Dans un premier temps, les déformations pariétales ont été appliquées aux tubes interne et externe : différents déphasages longitudinaux et angulaires entre ces deux déformations ont été étudiés pour optimiser les performances thermo-hydrauliques. La seconde configuration combine des déformations sur la paroi externe et un swirl sur la paroi interne de la géométrie. Cette configuration particulière permet en régime laminaire d’augmenter significativement le mélange du fait de l’apparition d’advection chaotique dans l’écoulement. Cette dernière géométrie est appliquée dans le cas d’un échangeur solaire à concentration et permet d’améliorer les performances par rapport à un tube lisse dans des conditions similaires. La dernière partie de l’étude est consacrée à une validation expérimentale des résultats numériques lorsque les déformations sont appliquées à une plaque. Des mesures par PIV et LDA ont été réalisées pour mesurer la vitesse locale de l’écoulement. / The work presented here is focused on the numerical study of specific successive wall deformations in alternate directions, applied to a tubular geometry. Those deformations help modifying the flow structure and thus its heat transfer and mixing properties. One of the main aims of the study is to apply those deformations to multifunctional exchangers which are heat exchangers and chemical reactors at the same time. The study is mainly focused on laminar flows and all the numerical calculations were performed using the CFD code ANSYS Fluent. The first step of the study is to assess the secondary flow created by the wall deformations. The influence of several deformation geometrical parameters has also been studied. In order to enhance the mixing in the deformed tube, the wall deformations have been applied to coaxial configurations (often used in the industry). Two kinds of annular configurations have been evaluated. At first, the wall deformations are applied to the external and internal walls of the coaxial tube. The effect on the heat transfer enhancement of the longitudinal and angular phase-shifting between the two deformations has been specifically assessed. The second configuration considered combines the alternate deformations on its external walls and a swirled internal wall. This particular annular configuration creates chaotic advection in laminar flows, therefore helping increasing the mixing. This geometry is used as a solar captor and helps increasing the global performances when compared with a smooth tube usually used. The last part of the presented work is focused on the experimental validation of the numerical results. Techniques such as PIV and LDA are used to measure local velocity fields in a plane duct with alternate deformations applied to its lower wall.

Negative cloud-to-ground (CG) lightning flashes transport negative charge from cloud to ground. Negative ground flashes typically involve various processes identified as preliminary breakdown, stepped leader, return stroke, dart leader, dart-stepped leader, subsequent return stroke, and cloud activity between strokes, such as regular pulse trains and chaotic pulse trains. These processes can be identified through their electromagnetic field signatures. The main focus of this thesis is to document the features and understand the origin of electromagnetic fields, especially the chaotic pulse trains, generated by lightning flashes. Electric field measurements have been used to study lightning flashes in Sweden. The equipment was a parallel flat plate antenna with an analog filter buffer circuit, connected to a digital high speed oscilloscope. Four simultaneous measurements were made: wideband measurement of the E-field (the vertical component) and its time derivative dE/dt, and two narrowband measurements of the E-field, centred around 3 MHz and 30 MHz. Fourier and wavelet transforms were used in the analysis of the measured data. The results show that preliminary breakdown pulses are stronger radiators at 3 MHz and 30 MHz than are the return strokes. A comparison of our results with those of previous studies obtained in different geographical regions clearly shows that the strength of preliminary breakdown pulses decreases with decreasing latitude. It is higher in the temperate regions (Sweden, for instance) and lower in the tropical regions. A comparison of the time derivatives of preliminary breakdown pulses and of the narrow bipolar pulses shows that the physical origin of these two types of pulse is different, even though they may have similar appearances in the broadband fields. This thesis introduces a new procedure to estimate the zero-crossing time of the lightning-generated radiation fields. The procedure is based on the fact that the time integral of the radiation fields generated by a discharge event whose duration is finite is equal to zero, and the zero-crossing time corresponds to the time when the peak of the integral is reached. In addition to tabulating the various statistical parameters and features of Chaotic Pulse Trains (CPTs), it is shown that these pulse trains are created by the simultaneous propagation of several dart-stepped leader type discharges in the cloud. Each dart-stepped leader type discharge generates a Regular Pulse Train (RPT), and these pulse trains combine randomly in time to generate CPTs. This conclusion is based on the results obtained by numerical simulations and by analysing the signatures of these pulse trains using Fourier and wavelet transformations. The results presented in this thesis show that electromagnetic fields, even those measured from a single station, can be used to extract information concerning the physical processes that gave rise to these fields.

La stéganographie est l’art de la dissimulation de l’information secrète dans un médium donné (cover) de sorte que le médium résultant (stégo) soit quasiment identique au médium cover. De nos jours, avec la mondialisation des échanges (Internet, messagerie et commerce électronique), s’appuyant sur des médiums divers (son, image, vidéo), la stéganographie moderne a pris de l’ampleur. Dans ce manuscrit, nous avons étudié les méthodes de stéganographie LSB adaptatives, dans les domaines spatial et fréquentiel (DCT, et DWT), permettant de cacher le maximum d’information utile dans une image cover, de sorte que l’existence du message secret dans l’image stégo soit imperceptible et pratiquement indétectable. La sécurité du contenu du message, dans le cas de sa détection par un adversaire, n’est pas vraiment assurée par les méthodes proposées dans la littérature. Afin de résoudre cette question, nous avons adapté et implémenté deux méthodes (connues) de stéganographie LSB adaptatives, en ajoutant un système chaotique robuste permettant une insertion quasi-chaotique des bits du message secret. Le système chaotique proposé consiste en un générateur de séquences chaotiques robustes fournissant les clés dynamiques d’une carte Cat 2-D chaotique modifiée. La stéganalyse universelle (classification) des méthodes de stéganographie développées est étudiée. A ce sujet, nous avons utilisé l’analyse discriminante linéaire de Fisher comme classifieur des vecteurs caractéristiques de Farid, Shi et Wang. Ce choix est basé sur la large variété de vecteurs caractéristiques testés qui fournissent une information sur les propriétés de l’image avant et après l’insertion du message. Une analyse des performances des trois méthodes de stéganalyse développées, appliquées sur des images stégo produites par les deux méthodes de stéganographie LSB adaptatives proposées, est réalisée. L’évaluation des résultats de la classification est réalisée par les paramètres: sensibilité, spécificité, précision et coefficient Kappa. / Steganography is the art of the dissimulation of a secret message in a cover medium such that the resultant medium (stego) is almost identical to the cover medium. Nowadays, with the globalization of the exchanges (Internet, messaging and e-commerce), using diverse mediums (sound, embellish with images, video), modern steganography is widely expanded. In this manuscript, we studied adaptive LSB methods of stéganography in spatial domain and frequency domain (DCT, and DWT), allowing of hiding the maximum of useful information in a cover image, such that the existence of the secret message in the stégo image is imperceptible and practically undetectable. Security of the message contents, in the case of its detection by an opponent, is not really insured by the methods proposed in the literature. To solve this question, we adapted and implemented two (known) methods of adaptive stéganographie LSB, by adding a strong chaotic system allowing a quasi-chaotic insertion of the bits of the secret message. The proposed chaotic system consists of a generator of strong chaotic sequences, supplying the dynamic keys of a modified chaotic 2D Cat map. Universal steganalysis (classification) of the developed methods of stéganography, is studied. On this question, we used the linear discriminating analysis of Fisher as classifier of the characteristic vectors of Farid, Shi and Wang. This choice is based on the wide variety of tested characteristic vectors that give an information about the properties of the image before and after message insertion. An analysis of the performances of three developed methods of steganalysis, applied to the produced stego images by the proposed adaptive methods of stéganography, is realized. Performance evaluation of the classification is realized by using the parameters: sensibility, specificity, precision and coefficient Kappa.

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.

Ce travail porte sur l'optimisation de la géométrie de chambre réverbérante en s'inspirant du concept de cavité chaotique. Les chambres réverbérantes (RC) sont de plus en plus utilisées comme moyen de test de compatibilité électromagnétique. Elles sont utilisées au-delà d'une fréquence minimale à parti de laquelle les champs sont, dans le volume central de la cavité, statistiquement homogènes et isotropes ; l'obtention de ces propriétés statistiques nécessite l'utilisation d'un mécanisme de brassage, pouvant être mécanique ou électronique. Or, dans les cavités chaotiques, la plupart des modes sont associés à des champs statistiquement homogènes et isotropes, et ceci sans avoir recours à aucun brassage. C'est pourquoi un rapprochement entre chambres réverbérantes et cavités chaotiques a été fait dans ce travail.En premier lieu, nous nous intéressons à des cavités chaotiques 2D obtenues par des modifications successives d'une cavité rectangulaire. Les mesures effectuées dans ces cavités à l'aide d'une théorie perturbative, validées par des résultats de simulation, montrent qu'un champ électrique homogène est obtenu. Les principes retenus pour modifier la géométrie de la cavité rectangulaire seront repris dans les cavités 3D.Les propriétés de trois cavités 3D obtenues en modifiant une cavité parallélépipédique sont étudiées et comparées à celles d'une chambre réverbérante classique munie d'un brasseur de modes. Les modes propres et fréquences de résonance sont déterminés pour ces quatre cavités à l'aide du logiciel HFSS d'Ansoft, tout d'abord en considérant des cavités de géométrie figée, puis en y incluant un brassage mécanique.L'étude de l'homogénéité et de l'isotropie des modes propres montre clairement que les meilleures performances sont obtenues pour une des cavités chaotiques proposées, et ceci quels que soient les critères utilisés.Par ailleurs, il est montré que, dans la chambre réverbérante classique, un grand nombre de modes présente une forte localisation spatiale de l'énergie électrique, alors que ce phénomène ne se produit pas dans la cavité chaotique retenue. Ce phénomène, non détectable par les mesures classiquement effectuées en chambre réverbérante, est dommageable à l'obtention des propriétés d'homogénéité et d'isotropie requises dans le volume de travail.Enfin, l'étude de la distribution des écarts entre fréquences de résonance montre, comme prédit par la Théorie des Matrices Aléatoire, une concordance entre le suivi de la loi asymptotique prévue dans une cavité chaotique et les propriétés d'homogénéité et d'isotropie des champs. Ceci ouvre la voie vers l'utilisation de critères de caractérisation basés sur les fréquences de résonance et non plus uniquement sur les distributions des champs / This work deals with the optimization of the geometry of a reverberation chamber, drawing inspiration from the concept of chaotic cavity. Reverberation chambers, widely used for electromagnetic compatibility tests, are used above a minimal frequency from which the fields are statistically isotropic and uniform; however to respect these properties, a mode stirring process is necessary, that can be mechanical or electronic. As, in chaotic cavities, most modes are isotropic and uniform without the help of any stirring process, we take advantage of the knowledge gained from the studies of chaotic cavities to optimize reverberation chamber behavior.We firstly consider 2D chaotic cavities obtained by modifying a rectangular cavity. Measurements besed on a perturbative approch, and validated by simulations, show uniformly distributed electric fields. Similar geometrical modifications are then proposed in 3D.Three 3D different geometries of cavities obtained from a 3D rectangular cavity are then studied, and their properties are compared with those of a classical reverberation chamber equipped witdh a mode stirrer. Eigenmodes and resonant frequencies are determined numerically using Ansoft HFSS software, first by considering fixed cavity geometries, then by moving the stirrer.Electric field uniformity and isotropy are studied using several criteria; all of them clearly show that the best performances are attained within one of the proposed chaotic cavities.Moreover, a strong energy localization effect appears for numerous modes in the classical reverberation chamber, whereas it is not observed in the proposed 3D chaotic cavity. This effect, never reported in reverberation chamber studies, affects the field uniformity and isotropy within the working volume.The cavities properties are also compared width respect to their eigenfrequency spacing distributions. As predicted by the Random matrix Theory, the best agrement width the asymptotic law associated to chaotic cavities corresponds to the best field properties in terms of uniformity and isotropy. It leads to the proposal of reverberation chamber characterization criteria based on resonant frequencies instead of field distributions

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-07-11T13:06:08Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) TeseJoseversaoCD.pdf: 2349040 bytes, checksum: f9cf2bfb304c798e864da4edd16e3a90 (MD5) / Made available in DSpace on 2017-07-11T13:06:08Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) TeseJoseversaoCD.pdf: 2349040 bytes, checksum: f9cf2bfb304c798e864da4edd16e3a90 (MD5) Previous issue date: 2016-02-26 / CNPQ / Geradores de números pseudo-aleatórios são amplamente utilizados em aplicações científicas e tecnológicas. Particularmente em criptografia, estes são empregados em sistemas de chave secreta, como geradores de sequências de cifragem. Neste trabalho, propomos algumas metodologias para o projeto destes geradores a partir de mapas caóticos. A primeira é baseada em duas técnicas: salto de amostras e discretização codificada variante no tempo. Mostra-se que o procedimento possui alta taxa de geração de bits por amostra caótica quando comparado com a codificação fixa no tempo, além de dispensar pós-processamento para melhoria de suas propriedades aleatórias. A outra metodologia utilizada é o emprego de sequências-m para eliminar a correlação residual na sequência codificada. A discretização variante no tempo apresenta uma característica de correlação bem definida que é aproveitada por um novo bloco de pós-processamento que utiliza sequências-m de menor complexidade linear que a metodologia anterior. Validam-se os métodos propostos empregando a bateria de teste NIST. / Random number generators are widely used in scientific and technological applications. Particularly in cryptography, they are used in secret-key systems, such as key sequence generators. In this work, we present two methodologies for the design of these generators from chaotic maps. The first one is based on two techniques: Skipping and time-varying coded discretization. We show that the proposed method has higher bit generation rate when compared to fixed-time coded discretization and dispenses post-processing in order to improve their random properties. Another methodology is the use of m-sequences to eliminate the residual correlation of the coded sequence. The time-varying coded discretization has a well-defined correlation characteristic that is exploited by a new block ofpost-processing using m-sequences that requires less memory than the previous methodology. The effectiveness of this procedure is verified through the NIST test.

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.

We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of a continuous curve and controlling the geometry of the latter, we determine their Hausdorff and box-counting dimension and show that these take distinct values. Moreover, the same approach allows us to describe the topological structure of the attractors and to prove their minimality.

Diplomová práce pojednává o teorii chaotických dynamických systémů, speciálně se pak zabývá Rösslerovým systémem. Kromě standardních výpočtů spojených s bifurkační analýzou se práce zaměřuje na problém stabilizace, konkrétně na stabilizaci rovnovážných bodů. Ke stabilizaci je využita základní metoda zpětnovazebního řízení s časovým zpožděním. Významnou část práce tvoří zavedení a implementace obecné metody pro hledání vhodné volby parametrů vedoucí k úspěšné stabiliaci. Dalším diskutovaným tématem je možnost synchronizace dvou Rösslerových systémů pomocí různých synchronizačních schémat.