Unique equilibrium states for flows and homeomorphisms with non-uniform structure

By Vaughn Climenhaga, Daniel J. Thompson. 2015

86 citations recorded by the source corpus.

Abstract Using an approach due to Bowen, Franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property. We show that this conclusion remains true using weaker non-uniform versions of specification, expansivity, and the Bowen property. We also establish a corresponding result for homeomorphisms. In the homeomorphism case, we obtain the upper bound from the level-2 large deviations principle for the unique equilibrium state. The theory presented in this paper provides the basis for an ongoing program to develop the thermodynamic formalism in partially hyperbolic and non-uniformly hyperbolic settings.

Subfields: Computer Networks and Communications, Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7b6f70c4e070b0fb24e0ed4e1d179589a2c4f558

How researchers see this paper

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In Computer Networks and Communications

1. O. Sarig
2. S. Crovisier

In Condensed Matter Physics

1. Jérôme Buzzi
2. O. Sarig

In Mathematical Physics

1. Jérôme Buzzi
2. S. Crovisier
3. O. Sarig
4. S. Gouëzel
5. Vilton Pinheiro
6. Ian Melbourne
7. T. Jordan
8. Van Cyr

Citations in the corpus

• Measures of maximal entropy for surface diffeomorphisms (2018, background): “The first one is to observe that the non-uniform hyperbolicity and the homoclinic relations provide specification properties (going back to [16]) which may allow to work directly at the level of the manifold (this is the case for instance in the recent works [40, 41, 24]).”