For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials φ the topological pressure is entirely determined by the values of φ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-6,
author = {Katrin Gelfert and Christian Wolf},
title = {Topological Pressure for One-Dimensional Holomorphic Dynamical Systems},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {55},
year = {2007},
pages = {53-62},
zbl = {1115.37047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-6}
}
Katrin Gelfert; Christian Wolf. Topological Pressure for One-Dimensional Holomorphic Dynamical Systems. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 53-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-6/