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Fine Structures of Hyperbolic Diffeomorphisms (Paperback, 1st ed. Softcover of orig. ed. 2009)
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Fine Structures of Hyperbolic Diffeomorphisms (Paperback, 1st ed. Softcover of orig. ed. 2009)
Series: Springer Monographs in Mathematics
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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.
General
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