The study of hyperbolic systems is one of the core themes of modern dynamicalsystems. For dynamics on surfaces there is a particularly complete theory where the fine-scale structure of hyperbolic invariant sets and the measures theysupport can be described in a very complete and elegant way. The present book, written by leading mathematicians in the field, provides a largely self-contained, rigorous description of this theory. It plays an important role in filling a gap in the present literature on hyperbolic dynamics and is highly recommended for all PhD students interested in this field. By leading research teamon core topic in dynamical systems INDICE: 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.
- ISBN: 978-3-540-87524-6
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 380
- Fecha Publicación: 01/10/2008
- Nº Volúmenes: 1
- Idioma: Inglés