Topological Pressure for One-Dimensional Holomorphic Dynamical Systems

Volume 55 / 2007

Katrin Gelfert, Christian Wolf Bulletin Polish Acad. Sci. Math. 55 (2007), 53-62 MSC: 37F10, 37D25, 37D35, 28D20. DOI: 10.4064/ba55-1-6


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.


  • Katrin GelfertInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8, P.O. Box 21
    00-956 Warszawa, Poland
  • Christian WolfDepartment of Mathematics
    Wichita State University
    Wichita, KS 67260, U.S.A.

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