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Combinatorial group theory --- Hyperbolic groups --- Riemannian manifolds
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Hyperbolic spaces. --- Hyperbolic groups. --- Espaces hyperboliques --- Groupes hyperboliques --- Hyperbolic spaces --- Hyperbolic groups --- Espaces hyperboliques. --- Groupes hyperboliques.
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"Subset currents on hyperbolic groups were introduced by Kapovich and Nagnibeda as a generalization of geodesic currents on hyperbolic groups, which were introduced by Bonahon and have been successfully studied in the case of the fundamental group 1() of a compact hyperbolic surface . Kapovich and Nagnibeda particularly studied subset currents on free groups. In this article, we develop the theory of subset currents on 1(), which we call subset currents on . We prove that the space SC() of subset currents on is a measure-theoretic completion of the set of conjugacy classes of non-trivial finitely generated subgroups of 1(), each of which geometrically corresponds to a convex core of a covering space of . This result was proved by Kapovich-Nagnibeda in the case of free groups, and is also a generalization of Bonahon's result on geodesic currents on hyperbolic groups. We will also generalize several other results of them. Especially, we extend the (geometric) intersection number of two closed geodesics on to the intersection number of two convex cores on and, in addition, to a continuous R0-bilinear functional on SC()"--
Fuchsian groups. --- Riemann surfaces. --- Hyperbolic groups. --- Ergodic theory.
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Topological groups. Lie groups --- Hyperbolic groups. --- Groupes hyperboliques --- Tiling (Mathematics) --- Pavage (mathématiques) --- Cancellation theory (Group theory) --- Hyperbolic groups --- Combinatorial designs and configurations --- Mathematics --- Group theory --- Groupes hyperboliques.
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Group theory --- Combinatorial group theory --- Hyperbolic groups --- Groupes combinatoires, théorie des --- Congresses. --- Congresses. --- Congrès
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Group theory --- Geometry --- Combinatorial set theory --- Combinatorische groepentheorie --- Geometry [Hyperbolic ] --- Groupes [Theories des ] combinatoires --- Géométrie hyperbolique --- Meetkunde [Hyperbolische ] --- Hyperbolic groups. --- 51 --- Hyperbolic groups --- Mathematics --- 51 Mathematics --- Geometric group theory --- Groupes, Théorie géométrique des --- Groupes, Théorie des --- Géometrie hyperbolique
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Group theory --- 51 <082> --- Mathematics--Feestbundels. Festschriften --- 51 <082> Mathematics--Feestbundels. Festschriften --- Geometric group theory. --- Hyperbolic groups. --- Groupes, Théorie géométrique des --- Groupes hyperboliques --- Geometric group theory --- Hyperbolic groups --- Groupes, Théorie géométrique des. --- Groupes hyperboliques.
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Hyperbolic groups --- Groupoids --- Group theory. --- Duality theory (Mathematics) --- Groupes hyperboliques --- Groupoïdes --- Groupes, Théorie des --- Dualité, Principe de (Mathématiques) --- Group theory --- DUALITY THEORY (MATHEMATICS) --- Théorie des groupes --- Groupoïdes --- Théorie des groupes --- Dualité, Principe de (Mathématiques)
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Group theory --- Differential geometry. Global analysis --- Differentiable dynamical systems --- Differentieerbare dynamicasystemen --- Dynamique topologique --- Global differential geometry --- Groupes hyperboliques --- Géométrie différentielle globale --- Hyperbolic groups --- Hyperbolische groepen --- Meetkunde [Differentiaal globale ] --- Systèmes dynamiques différentiables --- Topological dynamics --- Topologische dynamica --- Global differential geometry. --- Hyperbolic groups. --- Differentiable dynamical systems. --- 51 --- Dynamics, Topological --- Geometry, Differential --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Mathematics --- 51 Mathematics --- Topological dynamics.
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The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. More than half of the material appears here for the first time in book form, describing many recent developments in the area such as topics on irregular sets, variational principles, applications to number theory, measures of maximal dimension, multifractal nonrigidity, and quantitative recurrence. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained and directed to researchers as well as graduate students that wish to have a global view of the theory together with a working knowledge of its main techniques. It will also be useful as as basis for graduate courses in dimension theory of dynamical systems, multifractal analysis, and pointwise dimension and recurrence in hyperbolic dynamics.
Differentiable dynamical systems. --- Hyperbolic groups. --- Dimension theory (Topology) --- Topology --- Group theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Cell aggregation --- Global analysis (Mathematics). --- Dynamical Systems and Ergodic Theory. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Analysis. --- Mathematics. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Dynamics. --- Ergodic theory. --- Manifolds (Mathematics). --- Complex manifolds. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics
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