Dimension and Recurrence in Hyperbolic Dynamics

Barreira, Luis

ISBN 10: 3764388811 / ISBN 13: 9783764388812

Published by Birkhauser Verlag AG, 2008

This book offers a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It examines the interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. Series: Progress in Mathematics. Num Pages: 300 pages, biography. BIC Classification: PBPH. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 234 x 156 x 19. Weight in Grams: 643. . 2008. Hardback. . . . . Seller Inventory # V9783764388812

Synopsis:

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.

From the Back Cover:

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.

Bibliographic Details

Title: Dimension and Recurrence in Hyperbolic ...
Publisher: Birkhauser Verlag AG
Publication Date: 2008
Binding: Hardcover
Condition: New