Unique equilibrium states for Bonatti-Viana diffeomorphisms

V. Climenhaga; T. Fisher; D. J. Thompson

Unique equilibrium states for Bonatti-Viana diffeomorphisms

Dynamical Systems 2018-02-23 v4

Authors: V. Climenhaga , T. Fisher , D. J. Thompson

Abstract

We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potentials. In particular, we characterize the SRB measure as the unique equilibrium state for a suitable geometric potential. The techniques developed are applicable to a wide class of DA diffeomorphisms, and persist under $C^1$ perturbations of the map. These results are an application of general machinery developed by the first and last named authors.

Keywords

unique equilibrium states Bonatti-Viana diffeomorphisms SRB measure geometric potential DA diffeomorphisms C^1 perturbations robust transitivity

Cite

@article{arxiv.1505.06371,
  title  = {Unique equilibrium states for Bonatti-Viana diffeomorphisms},
  author = {V. Climenhaga and T. Fisher and D. J. Thompson},
  journal= {arXiv preprint arXiv:1505.06371},
  year   = {2018}
}

Comments

46 pages, 2 figures. In response to referee reports, we added an appendix on the regularity of the geometric potential, and made other suggested minor changes. Accepted for publication in Nonlinearity

Unique equilibrium states for Bonatti-Viana diffeomorphisms

Abstract

Keywords

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