| Fine Structures of Hyperbolic Diffeomorphisms 2009 Edition Contributor(s): Pinto, Alberto Adrego (Author), Rand, David A. (Author), Ferreira, Flávio (Author) |
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ISBN: 3540875247 ISBN-13: 9783540875246 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: October 2008 Annotation: The study of hyperbolic systems is one of the core themes of modern dynamical systems. For dynamics on surfaces there is a particularly complete theory where the fine-scale structure of hyperbolic invariant sets and the measures they support can be described in a very complete and elegant way. The present book, written by leading mathematicians in the field, provides a largely self-contained, rigorous description of this theory. It plays an important role in filling a gap in the present literature on hyperbolic dynamics and is highly recommended for all PhD students interested in this field. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Science | Physics - Mathematical & Computational - Mathematics | Mathematical Analysis |
| Dewey: 515.39 |
| LCCN: 2008935620 |
| Series: Springer Monographs in Mathematics |
| Physical Information: 1.02" H x 9.26" W x 6.44" (1.46 lbs) 354 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |