Fine Structures of Hyperbolic Diffeomorphisms - Pinto, Alberto Adrego

Résumé :
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 Pint?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.

Biographie:

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.

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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

Sommaire:
HR structures.- Solenoid functions.- Self-renormalizable structures.- Rigidity.- Gibbs measures.- Measure scaling functions.- Measure solenoid functions.- Cocycle-gap pairs.- Hausdorff realizations.- Extended Liv?ic-Sinai eigenvalue formula.- Arc exchange systems and renormalization.- Golden tilings (in collaboration with J.P.?Almeida and A.?Portela).- Pseudo-Anosov diffeomorphisms in pseudo-surfaces.