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Fine Structures of Hyperbolic Diffeomorphisms
Springer Monographs in Mathematics
ISBN/EAN: 9783642099564
Umbreit-Nr.: 1128960
Sprache:
Englisch
Umfang: xvi, 354 S., 77 s/w Illustr., 354 p. 77 illus.
Format in cm:
Einband:
kartoniertes Buch
Erschienen am 25.11.2010
Auflage: 1/2010
- Zusatztext
- 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.
- Kurztext
- Inhaltsangabe1 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.