Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions
| Autor: | Díaz, L. J., Gelfert, K. |
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| Rok vydání: | 2010 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study a partially hyperbolic and topologically transitive local diffeomorphism $F$ that is a skew-product over a horseshoe map. This system is derived from a homoclinic class and contains infinitely many hyperbolic periodic points of different indices and hence is not hyperbolic. The associated transitive invariant set $\Lambda$ possesses a very rich fiber structure, it contains uncountably many trivial and uncountably many non-trivial fibers. Moreover, the spectrum of the central Lyapunov exponents of $F|_{\Lambda}$ contains a gap and hence gives rise to a first order phase transition. A major part of the proofs relies on the analysis of an associated iterated function system that is genuinely non-contracting. Comment: 45 pages, 4 figures |
| Databáze: | arXiv |
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