Phase transitions for uniformly expanding maps

Yakov Pesin; Ke Zhang

doi:10.1007/s10955-005-9005-7

Phase transitions for uniformly expanding maps

Yakov Pesin, Ke Zhang

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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.

Original language	English (US)
Pages (from-to)	1095-1110
Number of pages	16
Journal	Journal of Statistical Physics
Volume	122
Issue number	6
DOIs	https://doi.org/10.1007/s10955-005-9005-7
State	Published - Mar 2006

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-005-9005-7

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title = "Phase transitions for uniformly expanding maps",

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

author = "Yakov Pesin and Ke Zhang",

note = "Funding Information: We would like to thank Omri Sarig for numerous useful discussions we had with him while working on the paper. The work was partially supported by the National Science Foundation grant #DMS-0503810 and U.S.-Mexico Collaborative Research grant 0104675.",

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AU - Zhang, Ke

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N2 - 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.

AB - 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.

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JO - Journal of Statistical Physics

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Phase transitions for uniformly expanding maps

Abstract

All Science Journal Classification (ASJC) codes

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