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2003 | 176 | 2 | 97-125
Tytuł artykułu

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

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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.
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  • Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, U.S.A.
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bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-2-1
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