Made available in DSpace on 2016-12-23T14:34:49Z (GMT). No. of bitstreams: 1 Carla Rodrigues Almeida.pdf: 592195 bytes, checksum: 070fca888db010e772db2fafedfd378d (MD5) Previous issue date: 2012-08-13 / O objetivo deste trabalho é estudar as folheações que surgem a partir de estruturas de Nambu e apresentar a relação entre formas diferenciais e algumas destas estruturas. Mais precisamente, fazer um estudo da geometria de Poisson e de folheações singulares, enfatizando o caso da folheação simplética que surge da estrutura de Poisson e, em seguida, apresentar a geometria de Nambu, estudando o caso das folheações que surgem destas estruturas de ordem maiores ou iguais a três. Neste caso particular, vamos mostrar como tais estruturas de Nambu se relacionam com formas diferenciais e, por esta relação, classificar as estruturas de Nambu lineares através de um resultado de classificação de p-formas integráveis / The aim of this work is to study the foliations that arise from Nambu structures and present the relationship between differential forms and some of this structures. More specifically, to make a study of the Poisson geometry and of singular foliations, emphasiz-ing the case of the simplectic foliation that arises from the Poisson structure and then, to present the Nambu geometry, studying the case of the foliations that arise from the this structures of order grater than or equal to three. In this particular case, we shall show how this Nambu structures are related with differential formas and, by this relationship, classify linear Nambu structure through a result of classification of integrable differential p-forms

Neste trabalho estudamos relações entre expoente de Lyapunov e continuidade absoluta da folheação central para difeomorfismos parcialmente hiperbólicos conservativos de \'T POT. 3\'. Sobre tal tema, provamos que tipicamente (\'C POT. 1\' aberto e \'C POT. 2\' denso) os difeomorfismos parcialmente hiperbólicos, conservativos de classe \'C POT. 2\' , do toro \'T POT. 3\', apresentam folheação central não absolutamente contínua. Desta maneira, respondemos positivamente uma pergunta proposta em [20]. Também neste trabalho, estudamos entropia topológica para Sistema Iterado de Funções. Neste contexto, damos uma nova demonstração para uma conjectura proposta em [14] e provada primeiramente em [15]. Apresentamos um método geométrico que nos permite calcular entropia para transformações de \'S POT. 1\', como em [15]. Além de disso o método apresentado se verifica para casos mais gerais, como por exemplo: transformações não comutativas / In this work we study relations between Lyapunov exponents, absolute continuity of center foliation for conservative partially hyperbolic diffeomorphisms of \'T POT. 3\'. About this theme, (on a \'C POT. 1\' open and \'C POT. 2\'dense set) of conservative partially hyperbolic \'C POT. 2\' diffeomorphisms of the 3-torus presents non absolutely continuous center foliation. So, we answer positively a question proposed in [20]. Also in this work, we study topological entropy for Iterated Functions Systems. In this setting, we give a proof for a conjecture proposed in [14] and firstly proved in [15]. We present a geometrical method that allows us to calcule the entropy for transformations of \'S POT. 1\', like in [15]. Furthermore this method holds for more general cases, for example: non commutative transformations

This thesis examines the relation between classical and quantum mechanics from philosophical, mathematical and physical standpoints. It first presents arguments in support of "conjectural realism" in scientific theories distinguished by explicit contextual structure and empirical testability; and it analyses intertheoretic reduction in terms of weakly equivalent theories over a domain of applicability. Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum logic enable expression of the state geometry in Hilbert space. Quantum and classical mechanics are then elaborated and applied to subsystems and the measurement process. Consideration is also given to spacetime geometry and the constraints this places on the dynamics. Physics and Mathematics, it is argued, are growing apart; the inadequate treatment of approximations in general and localization in quantum mechanics in particular are seen as contributing factors. In the description of systems, the link between localization and lack of knowledge shows that quantum mechanics should reflect the domain of applicability. Restricting the class of states provides a means of achieving this goal. Localisation is then shown to have a mathematical expression in terms of compactness, which in tum is applied to yield a topological theory of bound and scattering states: Finally, the thesis questions the validity of "classical limits" and "quantisations" in intertheoretic reduction, and demonstrates that a widely accepted classical limit does not constitute a proof of reduction. It proposes a procedure for determining whether classical and quantum mechanics are weakly equivalent over a domain of applicability, and concludes that, in this restricted sense, classical mechanics reduces to quantum mechanics.

In the context of the Franks–Misiurewicz conjecture, we study homeomorphisms of the two-torus semiconjugate to an irrational rotation of the circle. As a special case, this conjecture asserts uniqueness of the rotation vector in this class of systems. We first characterize these maps by the existence of an invariant ‘foliation’ by essential annular continua (essential subcontinua of the torus whose complement is an open annulus) which are permuted with irrational combinatorics. This result places the considered class close to skew products over irrational rotations. Generalizing a well-known result of Herman on forced circle homeomorphisms, we provide a criterion, in terms of topological properties of the annular continua, for the uniqueness of the rotation vector. As a byproduct, we obtain a simple proof for the uniqueness of the rotation vector on decomposable invariant annular continua with empty interior. In addition, we collect a number of observations on the topology and rotation intervals of invariant annular continua with empty interior.

[pt] Neste trabalho estendemos os resultados em (12) e (22), sobre a minimalidade de uma das folheações estável ou instável forte), para o caso de atratores robustamente transitivos parcialmente hiperbólico e com direção central unidimensional. No nosso contexto a hiperbolicidade parcial esta definida somente no atrator. Algumas consequências são obtidas tais como a verificação de que estes atratores são robustamente) classes homoclínicas, possuem robustamente) interior vazio e admitem uma decomposição espectral. Resultados similares ainda valem no caso de atratores genericamente transitivos. / [en] In this work we extend the results in (12) and (22) about the minimality of one of the strong foliations (stable or unstable), for the case of robustly transitive attractors that is partially hyperbolic with one dimensional center bundle. In our context the partial hyperbolicity is defined only in the attractor. Some consequences are obtained as the verification that these attractors are (robustly) homoclinic classes, have (robustly) empty interior and admit a spectral decomposition. Similar results still holds in the case of generically transitive attractors.

[pt] Um resultado clássico da teoria de grupos de Lie garante que as órbitas da ação adjunta de um grupo de Lie compacto interceptam um toro máximo ortogonalmente. Esta ação é um exemplo das chamadas ações polares. Ações polares são ações de grupos compactos de isometrias que admitem seções (subvariedades totalmente geodésicas que interceptam as órbitas ortogonalmente). Ações polares e subvariedades isoparamétricas são casos particulares das chamadas folheações riemannianas singulares com seções,assunto que é estudado nesta tese. Além de apresentarmos resultados sobre essas folheações singulares apresentamos também resultados sobre as chamadas aplicações transnormais (generalizações das aplicações isoparamétricas) destacando como estes objetos estão relacionados. / [en] It follows from the classical Lie group theory that the orbits of an adjoint action of a compact Lie group intercept a maximal toru in a orthogonal way. This is an example of the so called Polar Action. A compact isometric action is said to be Polar if it admits sections, i.e. totally geodesic submanifolds that intercept the orbits orthogonally. Polar Actions and isoparametric manifolds are examples of a more general structure, the so called singular Riemannian Foliation with Section, the main subject of the thesis. Besides the results about these singular foliations we show also some results about transnormal maps (generalization of isoparametric maps) and stress the its connections with the singulare riemannian foliation with section.

No description available.

Cette thèse est divisée en trois parties. Dans la première, on étudie des systèmes articulés (mécanismes formés de tiges rigides) dont l'espace ambiant n'est pas le plan, mais diverses variétés riemanniennes. On étudie la question de l'universalité des mécanismes : cette notion correspond à l'idée que toute courbe serait tracée par un sommet d'un mécanisme, et que toute variété différentiable serait l'espace de configuration d'un mécanisme. On étend les théorèmes d'universalité au plan de Minkowski, au plan hyperbolique et enfin à la sphère.Toute surface dans R^3 peut être aplatie selon l'axe des z, et la surface aplatie s'approche d'une table de billard dans R^2. Dans la seconde partie, on montre que, sous certaines hypothèses, le flot géodésique de la surface converge localement uniformément vers le flot de billard. De plus, si le billard est dispersif, les propriétés chaotiques du billard remontent au flot géodésique : on montre qu'il est alors Anosov. En appliquant ce résultat à la théorie des systèmes articulés, on obtient un nouvel exemple de systèmes articulé Anosov, comportant cinq tiges.Dans la troisième partie, on s'intéresse aux variétés munies de connexions localement métriques, c'est-à-dire de connexions qui sont localement des connexions de Levi-Civita de métriques riemanniennes ; on donne dans ce cadre un analogue du théorème de décomposition de De Rham, qui s'applique habituellement aux variétés riemanniennes. Dans le cas où une telle connexion préserve une structure conforme, on montre que cette décomposition comporte au plus deux facteurs ; de plus, lorsqu'il y a exactement deux facteurs, l'un des deux est l'espace euclidien R^q. La démonstration des résultats de cette partie passe par l'étude des feuilletages munis d'une structure de similitude transverse. Sur ces feuilletages, on montre un résultat de rigidité qui peut être vu indépendamment des autres: ils sont soit transversalement plats, soit transversalement riemanniens. / This thesis is divided into three parts. In the first part, we study linkages (mechanisms made of rigid rods) whose ambiant space is no longer the plane, but various Riemannian manifolds. We study the question of the universality of linkages: this notion corresponds to the idea that every curve would be traced out by a vertex of some linkage, and that any differentiable manifold would be the configuration space of some linkage. We extend universality theorems to the Minkowski plane, the hyperbolic plane, and finally the sphere.Any surface in R^3 can be flattened with respect to the z-axis, and the flattened surface gets close to a billiard table in R^2. In the second part, we show that, under some hypotheses, the geodesic flow of the surface converges locally uniformly to the billiard flow. Moreover, if the billiard is dispersing, the chaotic properties of the billiard also apply to the geodesic flow: we show that it is Anosov in this case. By applying this result to the theory of linkages, we obtain a new example of Anosov linkage, made of five rods.In the third part, we first consider manifolds with locally metric connections, that is, connections which are locally Levi-Civita connections of Riemannian metrics; we give in this framework an analog of De Rham's decomposition theorem, which usually applies to Riemannian manifolds. In the case such a connection also preserves a conformal structure, we show that this decomposition has at most two factors; moreover, when there are exactly two factors, one of them is the Euclidean space R^q. The proofs of the results of this part use foliations with transverse similarity structures. On these foliations, we give a rigidity theorem of independant interest: they are either transversally flat, or transversally Riemannian.

A belt of Early Proterozoic rocks crops out in the Cottonwood Cliffs area, northwest Arizona. The belt contains an eastern and a western assemblage separated by the Slate Mountain fault. The western assemblage consists of mafic to felsic metavolcanic rocks, metapelites, and metaconglomerates. The eastern assemblage consists of phyllites, felsic to intermediate metavolcanic rocks, metagraywackes, and metagabbro bodies. The belt is bounded to the east by foliated granodiorite. The Valentine granite intruded the belt on the west and north. Steeply-plunging lineations and fold axes, and northeast-trending vertical foliation dominate the structural fabric. The regional elongation direction is near-vertical, as indicated by mineral and pebble lineations, and is parallel to fold axes. Although only one deformational event is evident, the intensity of that event may have obliterated evidence of any earlier deformation. Tertiary basalts and the Peach Springs Tuff locally overly the metamorphic rocks. Cenozoic normal faults in the area are mostly of minor displacement.

La période à 2.1 Ga du Craton d'Afrique de l'Ouest est une période de production massive de leucogranites. Le batholite de Ferkessédougou (Côte d'Ivoire) est, tant du point de vue de sa localisation, de son extension, que de son histoire dans la littérature géologique, un élément majeur de l'interprétation de la géodynamique du Paléoprotérozoïque. Tour à tour considéré comme un granite de ride augéosynclinale puis un granite typique de collision de type moderne, il n'en demeure pas moins le jalon d'un accident crustal NNE-SSW important du Paléoprotérozoïque : le linéament GFB (Greenville-Ferkessédougou-Bobodioulasso). Son étude et son interprétation s'inscrivent dans le débat sur la validité de la tectonique des plaques à cette période. Par analyse satellitale, nous montrons que ce batholite de 400 km de long sur une cinquantaine de large est en fait constitué d'une grande quantité de plutons adjacents relativement proches pétrographiquement. Le contexte général de son encaissant métavolcanique et/ou métasédimentaire birimien (2.2 Ga à 2.1 Ga) faiblement déformé et épizonal ainsi que l'absence de déformations tangentielles additionnelles traduisent la faiblesse de l'épaississement crustal synchrone de sa genèse. Sa fabrique déterminée par analyse structurale classique et par analyse de susceptibilité magnétique est double. La première "magmatique" est le plus souvent coaxiale, d'orientation et de pendages variables. Elle dessine des trajectoires courbes et traduit la mise en place des plutons. Elle est l'équivalent de ce qui a été rapporté à la déformation D1 autour de granites anciens. La seconde, magmatique à post-solidus, beaucoup mieux réglée, souvent constrictive ou non-coaxiale, est l'image d'un champ de contrainte régional transcurrent qui se rapporte à la déformation D2 classique dans la chronologie du craton birimien. Les plutons du batholite granitique de Ferké sont syntectoniques de cette grande phase de raccourcissement (2.1 Ga à 2.07 Ga) du birimien. Le passage en revue des différents modèles de plutons, l'analyse du secteur SW de la Côte d'Ivoire présentant des dykes granites à deux micas et des faciès métamorphiques de plus haut grade, un survol des formations de l'Imataca au Surinam, ainsi que le bilan de l'analyse structurale, nous amènent à proposer un modèle 3D pour le batholite de Ferké. Il correspondrait à un ensemble de petits plutons de forme laccolithique engagés dans la croûte superficielle entre les métasédiments épizonaux birimiens dits "de bassin", des gneiss et micaschistes probablement d'âge compris entre 2.2 et 2.1 Ga. Ces plutons seraient alimentés par un faisceau de dykes issus de la fracturation par ouverture en pull-apart du bassin sédimentaire SASCA-Bandama-Bobodioulasso. La fusion de la croûte essentiellement de type ceinture verte/TTG (absence de traces de matériel archéen), à la verticale du bassin subsident, aura incorporé du matériel sédimentaire de bassin. L'apport de chaleur nécessaire à la compensation de la faiblesse de l'épaississement aurait été fourni par le jeu décrochant des fractures majeures des pull-aparts. La place nécessaire à la mise en place des plutons exige une montée de ces derniers à la fin de la période extensive à la faveur de multiples cauldron-subsidences. Les conditions et régimes des deux déformations principales impliquent un lapse de temps très court entre la stabilisation de l'ouverture des bassins et leur fermeture. Par ailleurs, la variation du niveau structural du Nord-Est vers le Sud-Ouest, en particulier vers la zone probable de l'équivalent-racine au Vénézuéla-Surinam, montre un approfondissement et le rapprochement d'une croûte archéenne vers le SW alors qu'elle n'était jusqu'à présent reconnue que vers l'Ouest (Guinée, Dorsale de Man) ou soupçonnée vers l'Est au Ghana.