Topological pressure for one-dimensional holomorphic dynamical systems
Dynamical Systems
2007-06-01 v1
Abstract
For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials h the topological pressure is entirely determined by the values of h 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.
Cite
@article{arxiv.0705.4572,
title = {Topological pressure for one-dimensional holomorphic dynamical systems},
author = {Katrin Gelfert and Christian Wolf},
journal= {arXiv preprint arXiv:0705.4572},
year = {2007}
}