Dimension and recurrence in hyperbolic dynamics

Author(s)

• Barreira, Luis

Bibliographic Information

Dimension and recurrence in hyperbolic dynamics

Luis Barreira

（Progress in mathematics, v. 272）

Birkhäuser, c2008

Note

Includes bibliographical references (p. [285]-295) and index

Description and Table of Contents

Description

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.

Table of Contents

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.

by "Nielsen BookData"

Details

• NCID: BA86593067
• ISBN:
  • 9783764388812
• LCCN: 2008929876
• Country Code: sz
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Basel ; Boston
• Pages/Volumes: xiv, 300 p.
• Size: 24 cm
• Classification:
  • LCC : QA614.8
  • DC22 : 514.7
• Subject Headings:
  • LCSH : Differentiable dynamical systems
  • LCSH : Hyperbolic groups
  • LCSH : Dimension theory (Topology)
• Parent Bibliography ID:
  • BA00018010