Fine Structures of Hyperbolic Diffeomorphisms / by Alberto A. Pinto, David A. Rand, Flávio Ferreira.

Springer eBooks

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.

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.

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