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Artykuły w czasopismach na temat "Théorie géométrique et ergodique de groupes"
Michel, Alain. "La réflexion de Poincaré sur l’espace, dans l’histoire de la géométrie". Articles 31, nr 1 (9.09.2004): 89–114. http://dx.doi.org/10.7202/008935ar.
Pełny tekst źródłaRozprawy doktorskie na temat "Théorie géométrique et ergodique de groupes"
Long, Yusen. "Diverse aspects of hyperbolic geometry and group dynamics". Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM016.
Pełny tekst źródłaThis thesis explores diverse topics related to hyperbolic geometry and group dynamics, aiming to investigate the interplay between geometry and group theory. It covers a wide range of mathematical disciplines, such as convex geometry, stochastic analysis, ergodic and geometric group theory, and low-dimensional topology, etc. As research outcomes, the hyperbolic geometry of infinite-dimensional convex bodies is thoroughly examined, and attempts are made to develop integral geometry in infinite dimensions from a perspective of stochastic analysis. The study of big mapping class groups, a current focus in low-dimensional topology and geometric group theory, is undertaken with a complete determination of their fixed-point on compacta property. The thesis also clarifies certain folklore theorems regarding the Gromov hyperbolic spaces and the dynamics of amenable groups on them. Last but not the least, the thesis studies the connectivity of the Gromov boundary of fine curve graphs, a combinatorial tool employed in the study of the homeomorphism groups of surfaces of finite type
Vidotto, Pierre. "Géométrie ergodique et fonctions de comptage en mesure infinie". Nantes, 2016. https://archive.bu.univ-nantes.fr/pollux/show/show?id=464a8384-3383-4967-897b-1160f1741b9a.
Pełny tekst źródłaWe study here some dynamical properties of manifolds M = X/ Γ, endowed with a pinched negative sectional curvature, where X is a Hadamard manifold and Γ = π 1(M) acts by isometries on X. More precisely, we consider divergent Schottky groups Γ whose Bowen-Margulis measure mΓ is infinite on the unit tangent bundle T1X/ Γ. We first define a coding of the action of Γ on the boundary of X, which will be useful to build a symbolic space associated with the geodesic flow. Then we precise the rate of mixing of the geodesic flow (gt)tϵR on T1X/ Γ In a second part, we study the number of closed geodesics on M with length ≤ R. Finally, we give an asymptotic for the orbital counting function # { y ϵ Γ | d(o, y o) ≤ R} when R goes to infinity
Carderi, Alessandro. "Théorie ergodique des actions de groupes et algèbres de von Neumann". Thesis, Lyon, École normale supérieure, 2015. http://www.theses.fr/2015ENSL0995/document.
Pełny tekst źródłaThis dissertation is about measured group theory, sofic entropy and operator algebras. More precisely, we will study actions of groups on probability spaces, some fundamental properties of their sofic entropy (for countable groups), their full groups (for Polish groups) and the amenable subalgebras of von Neumann algebras associated with hyperbolic groups and lattices of Lie groups. This dissertation is composed of three parts.The first part is devoted to the study of sofic entropy of profinite actions. Sofic entropy is an invariant for actions of sofic groups defined by L. Bowen that generalize Kolmogorov's entropy. The definition of sofic entropy makes use of a fixed sofic approximation of the group. We will show that the sofic entropy of profinite actions does depend on the chosen sofic approximation for free groups and some lattices of Lie groups. The second part is based on a joint work with François Le Maître. The content of this part is based on a prepublication in which we generalize the notion of full group to probability measure preserving actions of Polish groups, and in particular, of locally compact groups. We define a Polish topology on these full groups and we study their basic topological properties, such as the topological rank and the density of aperiodic elements. The third part is based on a joint work with Rémi Boutonnet. The content of this part is based on two prepublications in which we try to understand when the von Neumann algebra of a maximal amenable subgroup of a countable group is itself maximal amenable. We solve the question for hyperbolic and relatively hyperbolic groups using techniques due to Popa. With different techniques, we will then present a dynamical criterion which allow us to answer the question for some amenable subgroups of lattices of Lie groups of higher rank
Pinochet, Lobos Antoine. "Théorèmes ergodiques, actions de groupes et représentations unitaires". Thesis, Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0228.
Pełny tekst źródłaIn this thesis, we first study the notion of discrepance, which measures the rate of convergence of ergodic means. We prove estimations for the discrepancy of actions on the sphere, the torus and the Bernoulli shift, as well as for actions of locally compact groups. Moreover, we prove an inequality that allows us to locate these discrepancies in the larger framework of the Monte-Carlo method. We consider the action of the free group on the boundary of its Cayley tree. We prove a convergence theorem of some means associated with this action, that only preserves the class of the natural measures on this boundary. We recover the previously known result that the unitary representation associated to it is irreducible. We then investigate the Howe-Moore property. Groups that satisfy it have the property that whenever they act ergodically on some probability space, then the action is mixing ; unfortunately, this property is not stable by direct products. We formulate a generalization of the Howe-Moore property, relying on an axiomatization of the Mautner phenomenon, that allows us to treat the case of products. Finally, we prove that every lattice inherits the radial rapid decay property, and give an explicit example of a discrete group, endowed with a natural length function which is quasi-isometric to a word-length, that has RRD but doesn't have RD
Lim, Seonhee. "Comptage de réseaux et rigidité entropique pour les actions de groupes sur des arbres et des immeubles". Paris 11, 2006. http://www.theses.fr/2006PA112051.
Pełny tekst źródłaTalbi, Malik. "Inégalité de Haagerup et géométrie des groupes". Lyon 1, 2001. http://www.theses.fr/2001LYO10160.
Pełny tekst źródłaKondah, Abdelaziz. "Les Endomorphismes dilatants de l'intervalle et leurs perturbations aléatoires". Dijon, 1991. http://www.theses.fr/1991DIJOS036.
Pełny tekst źródłaFrancini, Camille. "Caractères de groupes algébriques sur Q et mesures invariantes sur les solénoïdes". Thesis, Rennes 1, 2020. http://www.theses.fr/2020REN1S078.
Pełny tekst źródłaThis thesis is divided in two parts in which the invariant probability measures on solenoids play a major role. The solenoids (that is a compact finite dimensional connected abelian group) are a natural generalization of the usual torus. In the first part, we will study the action of groups on a solenoid by affine transformation; we obtain a necessary and sufficient condition for the action of such a group to have the spectral gap property when the solenoid is provided with the Haar measure. In the second part we will study the trace and characters of algebraic groups over the field of rational numbers. The trace of a countable group are function of positive type on the group which are invariant under conjugation. The characters (that are the indecomposable traces in a certain way) are generalization of the usual characters of finite dimensional representations and intervene in the theory of operator algebra and in the study of invariant random subgroups. We begin with the classification of this characters in the case of unipotent groups. Then we extend this classification to general algebraic groups, using the study of the unipotent case et the establishment of the invariant measure on adelic solenoids
Batakidis, Panagiotis. "Déformation par quantification et théorie de Lie". Paris 7, 2009. http://www.theses.fr/2009PA077149.
Pełny tekst źródłaThe first two chapters review the necessary notions concerning nilpotent Lie algebras, and invariant differential operators. An overview of the existing results of Fujiwara, Corwin-Greenleaf & al. Related to the Duflo conjecture is given in details. The Kontsevich formulation of Deformation Quantization is also reviewed. The generalization for coisotropic submanifolds due to Cattaneo-Felder is also covered and the notion of the reduction algebra is defined. In the third chapter considering a nonzero character of a fixed Lie subalgebra of a general Lie algebra, we prove a Theorem stating that the reduction algebra of the affine space is isomorphic to a deformation of the algebra of invariant differential operators. An explicit formula of this isomorphism is given. Other reduction algebras are examined, and the relations between them and their specializations is described in details. In the forth chapter we calculate characters of the reduction algebra and its specialization thanks to triquantization diagrams and we give an explicit formula for this character. Using double induction, we prove that this character equals the character constructed with the Penney eigendistribution Finally we compute in full detail all the formulas introduced in the text for a 5-dimensional nilpotent Lie algebra. It is shown that the character formula obtained gives an isomorphism between reduction algebras containing the exponential of a differential operator of degree 3 with rational coefficients
Gillibert, Luc. "Aspect géométrique des groupes et des images : les G-graphes et la compression par hypergraphe". Caen, 2006. http://www.theses.fr/2006CAEN2066.
Pełny tekst źródłaThere are two main subject in this thesis : the G-graphs, or the geometrical aspect of the groups, and HLC, or the geometrical aspect of the images applied to the compression. The G-graphs are introduced by Alain Bretto and Alain Faisant in 2003 for studying the group isomorphism problem. But many others applications are possible. We first study the construction of the G-graphs and how groups informations can be visualised on the graph. We gives an algorithm for constructing G-graphs and some theorems for solving the G-graph recognition problem and for the characterisation of bipartite G-graphs. We presents an automatic tool for the recognition of G-graphs and we construct a list of common graphs being G-graphs (Heawood's, Möbius-Kantor's and Dyck's graphs, etc. ). We also work on the classification of symmetric graphs. With G-graphs it is possible to extend the Foster Census, the current reference for cubic symmetric graphs, from the order 768 to the order 1322. We establish some lists of cubic and guintic, symmetric and semisymmetric graphs. Finally we introduce a geometrical representation of the pictures based on rectangle hypergraph. This representation leads ton a lossless compression scheme very efficient on synthetic pictures and named HLC. We show that HLC can be combined with a generic data compression algorithm : PPMd. The choice of PPMd is motivated by an experimental study. We give some experimental results showing the efficiency of HLC+PPMd and we generalise HLC for near-lossless compression and 3D pictures