TY - JOUR

T1 - Equality of pressures for rational functions

AU - Przytycki, Feliks

AU - Rivera-Letelier, Juan

AU - Smirnov, Stanislav

PY - 2004/6

Y1 - 2004/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=2942704291&partnerID=8YFLogxK

U2 - 10.1017/S0143385703000385

DO - 10.1017/S0143385703000385

M3 - Article

AN - SCOPUS:2942704291

VL - 24

SP - 891

EP - 914

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 3

ER -