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Synopsis
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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About the Author
Alberto Pinto Awards& Honours:
2008 Recognition of the scientific merit of the works done in Psychology Sciences by the Psychology School of University of Minho
2007 Espinho Town hall Golden Medal by scientific merit
1984Prize Augusto Martins, University of Porto.
1981 One of the six winners of the Mini-Olympics of Mathematics in Portugal.
David Rand Awards& Honours
1986 Whitehead Prize of the London Mathematical Society.
1988 Wolfson Research Award.
1988 Founding editor of Nonlinearity
2004 Fellow, Institute of Mathematics and Its Applications (by invitation)
2005 Britten Lecturer. McMaster University
2006 EPSRC Senior Research Fellowship
From the Back Cover
The study of hyperbolic systems is a core theme of modern dynamics. On surfaces the theory of the fine 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 scientific works of the leading research workers in this field. This book fills 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.
"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date2008
- ISBN 10 3540875247
- ISBN 13 9783540875246
- BindingHardcover
- LanguageEnglish
- Number of pages370
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Fine Structures of Hyperbolic Diffeomorphisms
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Springer Berlin Heidelberg, 2008
ISBN 10: 3540875247
ISBN 13: 9783540875246
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Hardcover. Condition: Very good. Hardcover. Signed and inscrubed to previous owner by author in ink at front free endpaper. 9 1/2" X 6 1/2". xvi, 353pp. Very mild shelf wear to covers, corners, and edges of paper over boards. Pages are clean and unmarked. Binding is sound. ABOUT THIS BOOK: The study of hyperbolic systems is a core theme of modern dynamics. On surfaces the theory of the fine 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 scientific works of the leading research workers in this field. This book fills 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.(Publisher). Seller Inventory # 12620
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