Thermodynamic formalism, topological pressure, and escape rates for critically non-recurrent conformal dynamics

• Autorzy: Mariusz Urbański
• Języki publikacji: EN

Abstrakty

EN

We show that for critically non-recurrent rational functions all the definitions of topological pressure proposed in [12] coincide for all t ≥ 0. Then we study in detail the Gibbs states corresponding to the potentials -tlog|f'| and their σ-finite invariant versions. In particular we provide a sufficient condition for their finiteness. We determine the escape rates of critically non-recurrent rational functions. In the presence of parabolic points we also establish a polynomial rate of appropriately modified escape. This extends the corresponding result from [6] proven in the context of parabolic rational functions. In the last part of the paper we introduce the class of critically tame generalized polynomial-like mappings. We show that if f is a critically tame and critically non-recurrent generalized polynomial-like mapping and g is a Hölder continuous potential (with sufficiently large exponent if f has parabolic points) and the topological pressure satisfies P(g) > sup(g), then for sufficiently small δ >0, the function t↦ P(tg), t ∈ (1-δ,1+δ), is real-analytic.

Kategorie tematyczne

• 37D45: Strange attractors, chaotic dynamics
• 37F35: Conformal densities and Hausdorff dimension
• 37D35: Thermodynamic formalism, variational principles, equilibrium states
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 176
• Numer: 2
• Strony: 97-125

Daty

wydano

2003

Twórcy

autor

Mariusz Urbański

• Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, U.S.A.

Identyfikatory

DOI

10.4064/fm176-2-1