Equality of pressures for rational functions

Feliks Przytycki, Juan Rivera-Letelier, Stanislav Smirnov

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

We prove that for all rational functions f on the Riemann sphere and potential -t ln |f′|, t ≥ 0 all the notions of pressure introduced in Przytycki (Proc. Amer. Math. Soc. 351(5) (1999), 2081-2099) coincide. In particular, we get a new simple proof of the equality between the hyperbolic Hausdorff dimension and the minimal exponent of conformal measure on a Julia set. We prove that these pressures are equal to the pressure defined with the use of periodic orbits under an assumption that there are not many periodic orbits with Lyapunov exponent close to 1 moving close together, in particular under the Topological Collet-Eckmann condition. In Appendix A, we discuss the case t < 0.

Original languageEnglish
Pages (from-to)891-914
Number of pages24
JournalErgodic Theory and Dynamical Systems
Volume24
Issue number3
DOIs
Publication statusPublished - Jun 2004
Externally publishedYes

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