The equilibrium states for semigroups of rational maps |
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Authors: | Hiroki Sumi Mariusz Urbański |
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Affiliation: | (1) Department of Mathematics, Graduate School of Science, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan;(2) Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, USA |
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Abstract: | We consider the dynamics of skew product maps associated with finitely generated semigroups of rational maps on the Riemann sphere. We show that under some conditions on the dynamics and the potential function ψ, there exists a unique equilibrium state for ψ and a unique exp(P(ψ) − ψ)-conformal measure, where P(ψ) denotes the topological pressure of ψ. The research of M. Urbański was supported in part by the NSF Grant DMS 0400481. H. Sumi thanks University of North Texas for kind hospitality, during his stay there. |
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Keywords: | Rational semigroup Skew product Equilibrium state |
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