Fine Structures of Hyperbolic Diffeomorphisms

• Main Authors: Pinto, Alberto A. (Author), Rand, David A. (Author), Ferreira, Flv̀io. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Differentiable dynamical systems.; Differential Equations.; Differential equations, partial.; Mathematical physics.; Dynamical Systems and Ergodic Theory.; Partial Differential Equations.; Ordinary Differential Equations.; Mathematical and Computational Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-87525-3

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:

• 1 Introduction
• 2 HR structures
• 3 Solenoid functions
• 4 Self-renomalizable structures
• 5 Rigidity
• 6 Gibbs measures
• 7 Measure scaling functions
• 8 Measure solenoid functions
• 9 Cocycle-gap pairs
• 10 Hausdorff realizations
• 11 Extended Livsic-Sinai eigenvalue formula
• 12 Arc exchange systems and renormalizations
• 13 Golden tiling (in collaboration wtih J.P.Almeida and A.Portela)
• 14 Pseudo-Anosov diffeomorphisms in pseudo-surfaces
• Appendix A: Classifying C1+ structures on the real line
• Appendix B: Classifying C1+ structures on Cantor sets
• Appendix C: Expanding dynamics of the circle
• Appendix D: Markov maps on train tracks
• Appendix E: Explosion of smoothness for Markov families
• References
• Index.