Ergodic theory of equilibrium states for rational maps

M. Denker, M. Urbanski

Research output: Contribution to journalArticle

71 Scopus citations

Abstract

Let T be a rational map of degree d ³ 2 of the Riemann sphere ₵ = ₵ u{¥}. We develop the theory of equilibrium states for the class of Holder continuous functions/for which the pressure is larger than sup f. We show that there exist a unique conformal measure (reference measure) and a unique equilibrium state, which is equivalent to the conformal measure with a positive continuous density. The associated Perron-Frobenius operator acting on the space of continuous functions is almost periodic and we show that the system is exact with respect to the equilibrium measure.

Original languageEnglish (US)
Pages (from-to)103-134
Number of pages32
JournalNonlinearity
Volume4
Issue number1
DOIs
StatePublished - Feb 1 1991

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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