Fine Structures of Hyperbolic Diffeomorphisms

• Main Authors: Pinto, Alberto A. (Author), Rand, David A. (Author), Ferreira, Flávio (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Partial differential equations.; Physics.; Dynamical Systems and Ergodic Theory.; Partial Differential Equations.; Ordinary Differential Equations.; Theoretical, Mathematical and Computational Physics.

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...

Table of Contents:

• 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.