Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions

• Autorzy: Lorenzo J. Díaz , Katrin Gelfert
• Języki publikacji: EN

Abstrakty

EN

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 Λ 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 $F|_{Λ}$ 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.

Kategorie tematyczne

• 37D35: Thermodynamic formalism, variational principles, equilibrium states
• 37C29: Homoclinic and heteroclinic orbits
• 37D30: Partially hyperbolic systems and dominated splittings
• 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 216
• Numer: 1
• Strony: 55-100

Daty

wydano

2012

Twórcy

autor

Lorenzo J. Díaz

• Departamento de Matemática PUC-Rio, Marquês de São Vicente 225, Gávea, Rio de Janeiro 225453-900, Brazil

autor

Katrin Gelfert

• Instituto de Matemática UFRJ, Av. Athos da Silveira Ramos 149, Cidade Universitária, Ilha do Fundão, Rio de Janeiro 21945-909, Brazil

Identyfikatory

DOI

10.4064/fm216-1-2