Dimension and Recurrence in Hyperbolic Dynamics

Luis Barreira

$126.95 $101.37

Hardback

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English

Birkhauser Verlag AG
17 July 2008

Cybernetics & systems theory; Calculus & mathematical analysis; Topology; Analytic topology

Series: Progress in Mathematics

The main objective of this book is to give a broad uni?ed introduction to the study of dimension and recurrence inhyperbolic dynamics. It includes a disc- sion of the foundations, main results, and main techniques in the rich interplay of fourmain 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. This includes topics on irregular sets, var- tional principles, applications to number theory, measures of maximal dimension, multifractal rigidity, and quantitative recurrence. The book isdirected to researchersas well as graduate students whowish to have a global view of the theory together with a working knowledgeof its main techniques. It can also be used as a basis for graduatecourses in dimension theory of dynamical systems, multifractal analysis (together with a discussion of several special topics), and pointwise dimension and recurrence in hyperbolic dynamics. I hope that the book may serve as a fast entry point to this exciting and active ?eld of research, and also that it may lead to further developments.

By: Luis Barreira
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: 2008 ed.
Volume: 272
Dimensions: Height: 235mm, Width: 165mm, Spine: 19mm
Weight: 647g
ISBN: 9783764388812
ISBN 10: 3764388811
Series: Progress in Mathematics
Pages: 300
Publication Date: 17 July 2008
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Basic Notions.- Basic Notions.- Dimension Theory.- Dimension Theory and Thermodynamic Formalism.- Repellers and Hyperbolic Sets.- Measures of Maximal Dimension.- Multifractal Analysis: Core Theory.- Multifractal Analysis of Equilibrium Measures.- General Concept of Multifractal Analysis.- Dimension of Irregular Sets.- Variational Principles in Multifractal Analysis.- Multifractal Analysis: Further Developments.- Multidimensional Spectra and Number Theory.- Multifractal Rigidity.- Hyperbolic Sets: Past and Future.- Hyperbolicity and Recurrence.- Pointwise Dimension for Hyperbolic Dynamics.- Product Structure of Hyperbolic Measures.- Quantitative Recurrence and Dimension Theory.

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Dimension and Recurrence in Hyperbolic Dynamics

Luis Barreira

$126.95 $101.37

Hardback

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