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Stochastics and thermodynamics for equilibrium measures of holomorphic endomorphisms on complex projective spaces |
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| Authors: | Michał Szostakiewicz Mariusz Urbański Anna Zdunik |
| Affiliation: | 1. Institute of Mathematics of the Polish Academy of Sciences, Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University, ul. Pawińskiego 5a, Block D, 5th Floor, 02-106?, Warsaw, Poland 2. Department of Mathematics, University of North Texas, Denton, TX?, 76203-1430, USA 3. Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097?, Warsaw, Poland |
| Abstract: | It was proved by Urbański and Zdunik (Fund Math 220:23–69, 2013) that for every holomorphic endomorphism $f:{{mathbb { P}}}^krightarrow {{mathbb { P}}}^k$ of a complex projective space ${{mathbb { P}}}^k,kge 1$ , there exists a positive number $kappa _f>0$ such that if $J$ is the Julia set of $f$ (i.e. the support of the maximal entropy measure) and $phi :Jrightarrow {mathbb R}$ is a Hölder continuous function with $sup (phi )-inf (phi ) |
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