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Journal of Statistical Physics

, Volume 122, Issue 6, pp 1095–1110 | Cite as

Phase Transitions for Uniformly Expanding Maps

  • Yakov Pesin
  • Ke Zhang
Article

Abstract

Given a uniformly expanding map of two intervals we describe a large class of potentials admitting unique equilibrium measures. This class includes all Hölder continuous potentials but goes far beyond them. We also construct a family of continuous but not Hölder continuous potentials for which we observe phase transitions. This provides a version of the example in (9) for uniformly expanding maps.

Key Words

Expanding maps thermodynamical formalism equilibrium measures phase transitions 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUniversity Park, State CollegeUSA

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