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Fine Structures of Hyperbolic Diffeomorphisms

  • Kartonierter Einband
  • 372 Seiten
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The study of hyperbolic systems is one of the core themes of modern dynamical systems. This book plays an important role in fillin... Weiterlesen
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The study of hyperbolic systems is one of the core themes of modern dynamical systems. This book 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.

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.

By leading research team on core topic in dynamical systems


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

HR structures.- Solenoid functions.- Self-renormalizable structures.- Rigidity.- Gibbs measures.- Measure scaling functions.- Measure solenoid functions.- Cocycle-gap pairs.- Hausdorff realizations.- Extended Livic-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.


Titel: Fine Structures of Hyperbolic Diffeomorphisms
EAN: 9783642099564
ISBN: 3642099564
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Genre: Mathematik
Anzahl Seiten: 372
Gewicht: 563g
Größe: H235mm x B155mm x T20mm
Jahr: 2010
Auflage: 2009

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