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Catalogue Information
Field name	Details
Dewey Class	515.39
Dewey Class	515.48
Title	Dimension and Recurrence in Hyperbolic Dynamics ([Ebook]) / by Luis Barreira.
Author	Barreira, Luis
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 2008.
Physical Details	XIV, 300 pages : online resource.
Series	Progress in mathematics ; 272
ISBN	9783764388829
Summary Note	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.:
Contents note	Preface -- Introduction -- Basic Notions -- I. Dimension Theory -- Dimension Theory and Thermodynamic Formalism -- Repellers and Hyperbolic Sets -- Measures of Maximal Dimension -- II. Multifractal Analysis: Core Theory -- Multifractal Analysis of Equilibrium Measures -- General Concept of Multifractal Analysis -- Dimension of Irregular Sets -- Variational Principles in Multifractal Analysis -- III. Multifractal Analysis: Further Developments -- Multidimensional Spectra and Number Theory -- Multifractal Rigidity -- Hyperbolic Sets: Past and Future -- IV. Hyperbolicity and Recurrence -- Pointwise Dimension for Hyperbolic Dynamics -- Product Structure of Hyperbolic Measures -- Quantitative Recurrence and Dimension Theory.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-7643-8882-9
Links to Related Works	Subject References: Analysis . Cell aggregation . Differentiable dynamical systems . Dynamical systems and ergodic theory . Global analysis (Mathematics) . Manifolds and Cell Complexes (incl. Diff.Topology) . Authors: Barreira, Luis . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 515.39 . 515.48 . 515.39 (DDC 23) .

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Dimension and Recurrence in Hyperbolic Dynamics

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