Topological Pressure for One-Dimensional Holomorphic Dynamical Systems
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 53-62
MSC: 37F10, 37D25, 37D35, 28D20.
DOI: 10.4064/ba55-1-6
Abstract
For a class of one-dimensional holomorphic maps $f$ of the Riemann sphere we prove that for a wide class of potentials $\varphi$ the topological pressure is entirely determined by the values of $\varphi$ 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.
