Geodesic
Topological Pressure for One-Dimensional Holomorphic Dynamical Systems
Katrin Gelfert 1   ; Christian Wolf 2
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21 00-956 Warszawa, Poland
2 Department of Mathematics Wichita State University Wichita, KS 67260, U.S.A.
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 1, pp. 53-62 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba55-1-6
Keywords: class one dimensional holomorphic maps riemann sphere prove wide class potentials varphi topological pressure entirely determined values varphi repelling periodic points version classical result bowen hyperbolic diffeomorphisms holomorphic non uniformly hyperbolic setting

Katrin Gelfert  1   ; Christian Wolf  2

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8, P.O. Box 21 00-956 Warszawa, Poland
2 Department of Mathematics Wichita State University Wichita, KS 67260, U.S.A. 
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Katrin Gelfert; Christian Wolf. Topological
  Pressure for One-Dimensional Holomorphic Dynamical Systems. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 1, pp. 53-62. doi: 10.4064/ba55-1-6

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