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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2012 | 216 | 1 | 55-100

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

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.

55-100

wydano
2012

### Twórcy

autor
• Departamento de Matemática PUC-Rio, Marquês de São Vicente 225, Gávea, Rio de Janeiro 225453-900, Brazil
autor
• Instituto de Matemática UFRJ, Av. Athos da Silveira Ramos 149, Cidade Universitária, Ilha do Fundão, Rio de Janeiro 21945-909, Brazil