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.
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MSC Classification: 37D25; 37D35; 37E05; 37E10.
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Pesin, Y., Zhang, K. Phase Transitions for Uniformly Expanding Maps. J Stat Phys 122, 1095–1110 (2006). https://doi.org/10.1007/s10955-005-9005-7
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DOI: https://doi.org/10.1007/s10955-005-9005-7