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

100%

Díaz L., Gelfert K.

Fundamenta Mathematicae

2012

tom 216

nr 1

55-100

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.

Topological Pressure for One-Dimensional Holomorphic Dynamical Systems

100%

Gelfert K., Wolf C.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

tom 55

nr 1

53-62

For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials φ the topological pressure is entirely determined by the values of φ on the repelling periodic points of f. This is a version of a classical result of Bowen for hyperbolic diffeomorphisms in the holomorphic non-uniformly hyperbolic setting.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Fundamenta Mathematicae

2 Gelfert K.

1 Díaz L.

1 Wolf C.

1 2012

1 2007

Wyniki wyszukiwania

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

Topological Pressure for One-Dimensional Holomorphic Dynamical Systems