Topological pressure for one-dimensional holomorphic dynamical systems

Katrin Gelfert; Christian Wolf

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arXiv · 0705.4572

Topological pressure for one-dimensional holomorphic dynamical systems

Katrin Gelfert·Christian Wolf

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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.

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Katrin Gelfert, Christian Wolf. 2007-05-31. Topological pressure for one-dimensional holomorphic dynamical systems. https://arxiv.org/abs/0705.4572

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