Fine Structures of Hyperbolic Diffeomorphisms

Fine Structures of Hyperbolic Diffeomorphisms

Description

The study of hyperbolic systems is a core theme of modern dynamics. On surfaces the theory of the ?ne scale structure of hyperbolic invariant sets and their measures can be described in a very complete and elegant way, and is the subject of this book, largely self-contained, rigorously and clearly written. It covers the most important aspects of the subject and is based on several scienti?c works of the leading research workers in this ?eld. This book ?lls a gap in the literature of dynamics. We highly recommend it for any Ph.D student interested in this area. The authors are well-known experts in smooth dynamical systems and ergodic theory. Now we give a more detailed description of the contents: Chapter1.TheIntroductionisadescriptionofthemainconceptsinhyp- bolic dynamics that are used throughout the book. These are due to Bowen, Hirsch, Man' "e, Palis, Pugh, Ruelle, Shub, Sinai, Smale and others. Stable and r unstable manifolds are shown to beC foliated. This result is very useful in a number of contexts. The existence of smooth orthogonal charts is also proved. This chapter includes proofs of extensions to hyperbolic di?eomorphisms of some results of Man' "e for Anosov maps. Chapter 2. All the smooth conjugacy classes of a given topological model are classi?ed using Pinto's and Rand's HR structures. The a?ne structures of Ghys and Sullivan on stable and unstable leaves of Anosov di?eomorphisms are generalized.

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Details

Author(s)
Alberto Adrego Pinto, David A. J. Rand, Flávio Ferreira
Format
Hardback | 354 pages
Dimensions
155 x 235 x 25.91mm | 719g
Publication date
30 Nov 2008
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publication City/Country
Berlin, Germany
Language
English
Edition Statement
2009 ed.
Illustrations note
3 Tables, black and white; 77 Illustrations, black and white; XVI, 354 p. 77 illus.
ISBN10
3540875247
ISBN13
9783540875246