The equilibrium states for semigroups of rational maps

Details The equilibrium states for semigroups of rational maps The equilibrium states for semigroups of rational maps

2007-07-17

arxiv.org/abs/0707.2444v8

Monatsh. Math., 156 (2009), no. 4, 371--390

Mathematics

Dynamical Systems

23 pages

Scientific paper

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 \psi, there exists a
unique equilibrium state for \psi and a unique $\exp(\P(\psi)-\psi)$-conformal
measure, where P(\psi) denotes the topological pressure of \psi.

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