Este trabalho propõe direcionar o estudo de involuções para dois ramos de pesquisa dentro da teoria das Singularidades e de Sistemas Dinâmicos. Mais precisamente, tratamos sua interligação com diagramas divergentes de dobras e seu aparecimento nos sistemas dinâmicos discretos reversíveis. No primeiro, tratamos da importante relação entre a classificação de diagramas divergentes de dobras, digamos de s dobras, e a classificação de s-uplas de involuções associadas a estes diagramas. No segundo contexto, o estudo se volta para a questão sobre condições para a linearização simultânea de uma classe de pares de involuções e a obtenção de formas normais desses pares / This work proposes to address the study of involutions for two branches of research into the theory of Singularities and Dynamical Systems. More precisely, we treat its interconnection with divergent diagrams of folds and their appearance in discrete reversible dynamical systems. First, we treat the important relationship between the classification of divergent diagrams of folds, say s folds, and the classification of s-tuples of involutions associated with these diagrams. In the second context, the study turns to the question of conditions for simultaneous linearization of a class of pairs of involutions and the deduction of the normal forms of these pairs

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-03-22T12:41:12Z No. of bitstreams: 1 robledoestevessantospires.pdf: 1489508 bytes, checksum: 70622a2c796a7c60cf73b540110f1a2f (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-04-24T02:20:57Z (GMT) No. of bitstreams: 1 robledoestevessantospires.pdf: 1489508 bytes, checksum: 70622a2c796a7c60cf73b540110f1a2f (MD5) / Made available in DSpace on 2016-04-24T02:20:57Z (GMT). No. of bitstreams: 1 robledoestevessantospires.pdf: 1489508 bytes, checksum: 70622a2c796a7c60cf73b540110f1a2f (MD5) Previous issue date: 2013-03-25 / A superlativação de conceitos por meio de projeções figurativas é um fenômeno muito comum à Língua Portuguesa, observado tanto na modalidade escrita quanto oral, e promove a emergência de padrões construcionais com sofisticados mecanismos de estruturação conceptual e formal. O presente estudo identifica, descreve e analisa um desses padrões: a Construção Hiperbólica por Símile – CHS, com especial destaque para as instâncias desta construção instituídas a partir do articulador sintático que nem, como ilustra o elenco de types a seguir: (1) A pobreza é que nem um câncer; (2) Passou por mim que nem um rabo de vento e (3) Inocência enrubesceu que nem uma romã. O aporte teórico central deste estudo advém de dois dos mais relevantes modelos da Linguística Cognitiva, quais sejam, a Gramática das Construções como um Modelo Baseado no Uso (GOLDBERG, 1995, 2006; LAKOFF, 1987; SALOMÃO, 2002-2007, 2009; MIRANDA, 2008-2010; BOAS, 2010) e a Semântica de Frames (FILLMORE, 1968, 1977, 1982), cujas teses apontam para a relevância do uso linguístico e da experiência (de todas as ordens) na arquitetura cognitiva do léxico e da gramática. Nesse enquadre, opta-se por procedimentos metodológicos baseados em corpora e em padrões de frequência de ocorrência e de tipos (GOLDBERG, 2006; BYBEE, 2007; CROFT & CRUSE, 2004). Os resultados certificam o valor semântico-pragmático específico dessas expressões hiperbólicas do Português, assegurando-lhes o estatuto de instâncias de um padrão construcional (a CHS) integrado por três subpadrões. Trata-se de uma construção vinculada à Construção Genérica de Modificação de Grau e cujo constructo ( FILLMORE, GOLDMAN & RHODES, 2010) se desenha pela presença de dois Elementos da Construção (EC): um EC Escopo ou núcleo graduável e um sintagma complexo (EC Qualificador_de_grau) resultante da ampliação de valência do EC Escopo. Evocando o frame Posição_máxima_em_uma_escala, a CHS tem seu Valor_hiperbólico assegurado através da comparação por Símile. Em termos de sua função discursiva, esta construção evocada por que nem, marcadamente informal, seja em modalidade oral ou escrita, demarca o domínio da autoexpressão, da subjetividade nas molduras interativas. / The construction of superlative concepts through figurative projections is a very common phenomenon to Portuguese Language, observed both in written and oral speech, and promotes the emergence of constructional patterns with sophisticated mechanisms for structuring conceptual and formal a language pattern. This study identifies, describes and analyzes one of these patterns: the Hyperbolic Construction by Simile – CHS, with special emphasis on its instances instituted by the syntactic articulator que nem, as illustrates the following types: (1) A pobreza é que nem um câncer; (2) Passou por mim que nem um rabo de vento e (3) Inocência enrubesceu que nem uma romã. The central theoretical assumptions comes from two of the most relevant models developed inside Cognitive Linguistics, namely the Construction Grammar as Used-based Model (GOLDBERG, 1995, 2006, LAKOFF, 1987; SOLOMÃO, 2002-2007, 2009; MIRANDA, 2008-2010; BOAS, 2010) and Frame Semantics (FILLMORE, 1968, 1977, 1982), whose thesis point to the importance of the language use and the experience (of all orders) in the cognitive architecture of the lexicon and grammar. In this framework, it is chosen a corpus-based methodological procedure, with the examination of token and type frequencies (GOLDBERG, 2006; BYBEE, 2007; CROFT & CRUSE, 2004). The results certify the specific semantic-pragmatic value of these hyperbolic expressions of Portuguese, assuring them the status of instances of a constructional pattern (the CHS) integrated for three subpatterns. The construction is linked to the Degree Modifying Generic Construction of which construct (FILLMORE, LEE-GOLDMAN & RHODES, 2010) is drawn by the presence of two construction elements (CE): a CE SCOPE or a gradable core and a complex phrase (CE DEGREE_MODIFIER) resultant from the expansion of the CE SCOPE valence. Evoking the frame Position_on_a_scale, CHS has its Hyperbolic_value ensured by the comparison by Simile. In terms of its discursive function, this construction evoked by que nem, markedly informal, whether in oral or written form, demarcates the area of self expression and subjectivity in interactive frames.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-04-06T13:55:31Z No. of bitstreams: 1 pedroandrearroyosilva.pdf: 3231300 bytes, checksum: 51e0163236485b163a96fe6fafa4315e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-04-24T03:52:09Z (GMT) No. of bitstreams: 1 pedroandrearroyosilva.pdf: 3231300 bytes, checksum: 51e0163236485b163a96fe6fafa4315e (MD5) / Made available in DSpace on 2016-04-24T03:52:09Z (GMT). No. of bitstreams: 1 pedroandrearroyosilva.pdf: 3231300 bytes, checksum: 51e0163236485b163a96fe6fafa4315e (MD5) Previous issue date: 2013-07-17 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O principal objetivo deste trabalho é o estudo da sensibilidade às condições iniciais sobre fluxos seccional-Anosov em variedades compactas tridimensionais para os quais o conjunto maximal invariante é igual ao conjunto não errante. Veremos que em conjuntos hiperbólicos e fluxos Anosov temos sensibilidade às condições iniciais. Generalizando o conceito de hiperbolicidade estudaremos os fluxos seccional hiperbólicos e seccional Anosov. Para este último demonstraremos que todo campo vetorial próximo destes fluxos é sensível às condições iniciais. / The main objective of this work is the study about sensitivity to initial conditions on seccional- Anosov flows on compact 3-dimensional manifolds for which the maximal invariant set and nonwandering sets coincide. We will see that in hyperbolic set and Anosov flow we have sensitivity to initial conditions. Extending the notion of hyperbolicity we study seccional hyperbolic flows and seccional-Anosov flows. For the latter we show that every vector field close to one of these flows is sensitive with respect to initial conditions.

Orientadores: Reginaldo Palazzo Júnior, Cátia Regina de Oliveira Quilles Queiroz / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-25T14:53:45Z (GMT). No. of bitstreams: 1 Benedito_CintyaWinkdeOliveira_D.pdf: 1485856 bytes, checksum: 50adbb3cffa1343c4a0cd9b3d7586173 (MD5) Previous issue date: 2014 / Resumo: Na busca por novos sistemas de comunicações muitos trabalhos têm sido realizados com o objetivo de obter constelações de sinais e códigos geometricamente uniformes no plano hiperbólico. Neste contexto, nossa proposta é identificar uma estrutura algébrica e geométrica para que códigos e reticulados possam ser construídos neste espaço. O problema central deste trabalho consiste em construir grupos fuchsianos provenientes de tesselações hiperbólicas regulares {p,q} utilizando diversos tipos de emparelhamentos e identificá-los com álgebras e ordens dos quatérnios, definindo-os assim como aritmético. Desta forma, propomos um algoritmo para construir grupos fuchsianos aritméticos provenientes de tesselações hiperbólicas regulares {p,q} cujo polígono hiperbólico regular gera uma superfície orientada de gênero maior ou igual a dois. Para isso, fornecemos uma condição necessária para que estes grupos possam ser obtidos, esta condição será denominada condição de Fermat devido a sua identificação com os números de Fermat. Através da construção destes grupos, mostramos que existe um isomorfismo entre dois grupos fuchsianos aritméticos provenientes de uma tesselação {p,q} a partir de emparelhamentos diferentes. Além disso, descrevemos alguns dos corpos de números que utilizamos para construir grupos fuchsianos aritméticos, como subcorpos maximais reais de corpos ciclotômicos, a fim de propor uma relação entre os reticulados hiperbólicos e os reticulados euclidianos. Reticulados hiperbólicos completos obtidos através da identificação de grupos fuchsianos com ordens maximais dos quatérnios também são apresentados. Desta forma, obtemos um rotulamento completo dos pontos da constelação de sinal associada / Abstract: In the search for new communications systems many studies have been conducted with the goal of obtaining signal constellations and geometrically uniform codes in the hyperbolic plane. In this context, our proposal is to identify an algebraic and geometric structures for constructing codes and lattices in this space. The central problem of this work is to construct fuchsian groups derived from hyperbolic tessellations {p,q} using different edge-pairings sets and identify them with quaternion algebras and quaternion orders, by setting it as arithmetic. We also propose an algorithm to construct arithmetic fuchsian groups from a tessellation {p,q} whose regular hyperbolic polygon generates an oriented and compact surface with genus greater or equal than 2. For that we provide a necessary condition for these groups to be obtained, this necessary condition is called Fermat condition due to its identification with the Fermat numbers. By the construction of these groups, it is also shown an isomorphism between two arithmetic fuchsian groups derived from a tessellation {p,q} via different edge-pairings sets. Furthermore, we will describe some of the number fields that we use to construct arithmetic fuchsian groups as maximal real subfields of cyclotomic fields in order to propose a relationship between hyperbolic lattices and euclidean lattices. Complete hyperbolic lattices obtained by identifying fuchsian groups with maximal quaternion orders will also be presented. In this way we have a complete labeling of the points of the corresponding signal constellation / Doutorado / Telecomunicações e Telemática / Doutora em Engenharia Elétrica

Orientadores: Jaime Angulo Paiva, Marcia A. G. Scialom / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T09:39:02Z (GMT). No. of bitstreams: 1 Paiva_LynnyngsKellyArrudaSaraivade_D.pdf: 1499074 bytes, checksum: 7fef4b8257781913440ab95a338aedcc (MD5) Previous issue date: 2005 / Doutorado / Matematica / Doutor em Matemática

Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the Gromov-Hausdorff distance, is a theorem with many applications. In this thesis, we give a generalisation of this landmark result, more precisely, we give a compactness theorem for the space of distance measure spaces equipped with the generalised Gromov-Hausdorff-Levi-Prokhorov distance. A distance measure space is a triple (X, d,µ), where (X, d) forms a distance space (a generalisation of a metric space where, we allow the distance between two points to be infinity) and µ is a finite Borel measure. Using this result we prove that the Deligne-Mumford compactification is the completion of the moduli space of Riemann surfaces under the generalised Gromov-Hausdorff-Levi-Prokhorov distance. The Deligne-Mumford compactification, a compactification of the moduli space of Riemann surfaces with explicit description of the limit points, and the closely related Gromov compactness theorem for J-holomorphic curves in symplectic manifolds (in particular curves in an algebraic variety) are important results for many areas of mathematics. While Gromov compactness theorem for J-holomorphic curves in symplectic manifolds, is an important tool in symplectic topology, its applicability is limited by the lack of general methods to construct pseudo-holomorphic curves. One hopes that considering a more general class of objects in place of pseudo-holomorphic curves will be useful. Generalising the domain of pseudo-holomorphic curves from Riemann surfaces to Riemann surface laminations is a natural choice. Theorems such as the uniformisation theorem for surface laminations by Alberto Candel (which is a partial generalisation of the uniformisation theorem for surfaces), generalisations of the Gauss-Bonnet theorem proved for some special cases, and topological classification of “almost all" leaves using harmonic measures reinforces the usefulness of this line on enquiry. Also, the success of essential laminations, as generalised incompressible surfaces, in the study of 3-manifolds suggests that a similar approach may be useful in symplectic topology. With this motivation, we prove a compactness theorem analogous to the Deligne-Mumford compactification for the space of Riemann surface laminations.

Le problème de la limite continue de la gravitation quantique à boucle est encore ouvert. En effet, la dynamique précise n’est pas connue et nous ne disposons pas des outils nécessaires à l’étude de cette limite le cas échéant. Dans cette thèse, nous étudions quelques méthodes de coarse-graining (étude à gros grains) qui devraient contribuer à cette entreprise. Nous nous concentrons sur deux aspects du flot: la détermination d’observables naturelles à grandes échelles d’un côté et la manière de s’abstraire du problème de la dynamique à graphe variable en la projetant sur des graphes fixes de l'autre.Pour déterminer les observables aux grandes distances, nous étudions le cas des tétraèdres hyperboliques et leur description naturelle dans un langage proche de celui de la gravitation quantique à boucle. Les holonomies de surface en particulier jouent un rôle important. Cela dégage la structure des double spin networks constitués d'un graphe et de son dual, structure qui semble aussi apparaître dans les travaux de Freidel et al. Pour résoudre le problème des graphes variables, nous considérons et définissons les loopy spin networks. Ils encodent par des boucles la courbure locale d'un vertex effectif et permettent ainsi de décrire différents graphes en les masquant via le processus de coarse-graining. De plus, leur définition donne un procédé naturel systématique de coarse-graining pour passer d'une échelle à une autre.Ensemble, ces deux principaux résultats posent le fondement d'un programme de coarse-graining pour les théories invariantes sous difféomorphismes. / The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will investigate some coarse-graining methods that should become helpful in this enterprise. We concentrate on two aspects of the theory's coarse-graining: finding natural large scale observables on one hand and studying how the dynamics of varying graphs could be cast onto fixed graphs on the other hand.To determine large scale observables, we study the case of hyperbolic tetrahedra and their natural description in a language close to loop quantum gravity. The surface holonomies in particular play an important role. This highlights the structure of double spin networks, which consist in a graph and its dual, which seems to also appear in works from Freidel et al. To solve the problem of varying graphs, we consider and define loopy spin networks. They encode the local curvature with loops around an effective vertex and allow to describe different graphs by hidding them in a coarse-graining process. Moreover, their definition gives a natural procedure for coarse-graining allowing to relate different scales.Together, these two results constitute the foundation of a coarse-graining programme for diffeomorphism invariant theories.

Le contrôle des ondes électromagnétiques joue un rôle fondamental dans les technologies photoniques actuelles. De nos jours, on assiste à une demande croissante de composants agiles capable d'absorber efficacement les ondes électromagnétiques dans divers gamme de fréquences. Habituellement, ces absorbeurs s'appuient sur les résonances plasmoniques qui apparaissent dans les métaux nobles dans la gamme visible. Cependant, l'extension des propriétés plasmoniques aux spectres infrarouge et THz nécessite des matériaux adéquats ayant un comportement métallique à ces fréquences. Dans ce travail, nous étudions numériquement et expérimentalement les structures métal-isolant-métal (MIM) réalisées à partir de semi-conducteur hautement dopé Si: InAsSb qui a un comportement métallique dans la gamme infrarouge. Dans la deuxième partie, nous avons amélioré l'efficacité des résonateurs MIM en utilisant des métamatériaux hyperboliques qui miniaturisent les résonateurs. Dans la dernière partie, nous proposons un design universel ultra-mince qui permet de dépasser les contraintes associées au choix des matériaux et permettant la réalisation d'un absorbeur fonctionnant sur une gamme spectrale allant de l'infrarouge aux micro-onde. / The control of light absorbance plays a fundamental role in today's photonic technologies. And the urge to design and develop flexible structures that can absorb electromagnetic waves is very growing these days. Usually, these absorbers relies on plasmonic resonances that arise in noble metals in the visible range. However, the extension of the plasmonic properties to the infrared and THz spectra requires adequate materials that have a metallic behavior at these frequencies. In this work, we study numerically and experimentally the metal-insulator-metal (MIM) structures realized from highly doped semiconductor Si:InAsSb that has a metallic behavior in the infrared range. In the second, part we improved the efficiency of the MIM resonators by using hyperbolic metamaterials that also miniaturize the resonators. In the last part, we propose an ultra-thin universal design that overcomes the material barrier so that the total absorption can be achieved for different spectral ranges without changing the material.

Les systèmes hyperboliques interviennent dans de nombreuses branches des sciences : théorie cinétique, mécanique des fluides non visqueux, magnéto hydrodynamique, dynamique des gaz non visqueux, trafic routier, flux d’une rivière ou d’un glacier, processus de sédimentation, processus d’échanges chimiques, etc. Et souvent, les systèmes qui régissent ces évènements font intervenir des petits paramètres, dont l’étude asymptotique permet d’envisager des simplifications mathématiques et/ou informatiques notoires. L’existence locale et l’existence globale de solutions, uniformément par rapport à ces paramètres, sont des questions fondamentales. Cette thèse regroupe à la fois des résultats généraux sur l’existence locale uniforme de solutions pour des systèmes hyperboliques quasi-linéaires du premier ordre ; et sur l’existence globale uniforme de solutions autour d’un équilibre constant pour ces mêmes systèmes. Le cas du système d’Euler-Maxwell ne satisfaisant pas les conditions requises pour l’existence uniforme globale, nous le traitons à part. / Hyperbolic systems arise in a large field of sciences : kinetic theory, inviscid reactive flow, magnetohydrodynamics, inviscid gas dynamics, traffic flow, river or glacier flow, sedimentation processes, chemical exchange processes, etc. In these kind of systems, small paramaters often appear, and an asymptotic study may lead to mathematical or computational simplifications. One fundamental problem that we may work on is local and global existence of solutions for these systems, uniformly with respect to these parameters. This Ph.D. thesis includes, on one hand, general results on uniform local existence of solutions for first order quasi-linear hyperbolic systems ; and on the other hand, results on uniform global existence of solutions near constant equilibriums for these same systems. In the case of Euler-Maxwell systems, required conditions are not fulfilled for uniform global existence, then we treat it separately.

L’objectif de cette thèse est d’étudier et de donner des outils pour la compréhension des problèmes de perturbations singulières pour des modèles épidémiques et des problèmes de dynamiques de populations. Les modèles considérés sont des équations structurées en âge qui peuvent dans certains cas se réécrire comme des équations à retard. L’étude de ces classes d’exemples s’est faite avec succès et a permis de comprendre et de mettre en évidence toute la complexité et l’étendue de ces problèmes. Comme on peut le remarquer dans la littérature, l’une des clés fondamentales à la compréhension de ces problèmes est l’étude des variétés normalement hyperboliques en dimension infinie que nous avons largement étudiées dans cette thèse. L’approche utilisée est la méthode de Lyapunov-Perron. Ce qui nous a amené à étudier les problèmes de persistance et d’existence de trichotomie (dichotomie) exponentielle qui sont des éléments fondamentaux dans l’utilisation de cette méthode. / In this thesis we aim to give tools to understand singular perturbations in epidemic model sand population dynamic models. We study some singularly perturbed delay differential equation which does not enter into the class frame work of geometric singular perturbation for delay differential equations. An example of singularly perturbed age structured model is also studied. The study of these examples allowed us to understand and highlight some complexities of these problems. One of the main tools in understanding such questions is the normally hyperbolic manifolds theory which is our central focus in this thesis. The approach used here is the Lyapunov-Perron method. Therefore the problems of persistence and existence of exponential trichotomy (dichotomy) are also stressed since there are one of the mainingredients of this method.