The study of hyperbolic systems is a core theme of modern dynamics. On surfaces the theory of the fine 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 scientific works of the leading research workers in this field. This book fills 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.
Author(s): Alberto A. Pinto, David A. Rand, Flávio Ferreira (auth.)
Series: Springer Monographs in Mathematics
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2009
Language: English
Pages: 354
Tags: Dynamical Systems and Ergodic Theory;Partial Differential Equations;Ordinary Differential Equations;Mathematical and Computational Physics
Front Matter....Pages I-XVI
Introduction....Pages 1-20
HR structures....Pages 21-36
Solenoid functions....Pages 37-43
Self-renormalizable structures....Pages 45-53
Rigidity....Pages 55-72
Gibbs measures....Pages 73-84
Measure scaling functions....Pages 85-92
Measure solenoid functions....Pages 93-106
Cocycle-gap pairs....Pages 107-117
Hausdorff realizations....Pages 119-134
Extended Livšic-Sinai eigenvalue formula....Pages 135-141
Arc exchange systems and renormalization....Pages 143-159
Golden tilings (in collaboration with J.P. Almeida and A. Portela)....Pages 161-182
Pseudo-Anosov diffeomorphisms in pseudo-surfaces....Pages 183-199
Back Matter....Pages 201-353
