Buch, Englisch, 354 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 563 g
Buch, Englisch, 354 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 563 g
Reihe: Springer Monographs in Mathematics
ISBN: 978-3-642-09956-4
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
Weitere Infos & Material
HR structures.- Solenoid functions.- Self-renormalizable structures.- Rigidity.- Gibbs measures.- Measure scaling functions.- Measure solenoid functions.- Cocycle-gap pairs.- Hausdorff realizations.- Extended Livšic-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.
