English

Equilibrium states for Ma\~n\'e diffeomorphisms

Dynamical Systems 2017-10-25 v2

Abstract

We study thermodynamic formalism for the family of robustly transitive diffeomorphisms introduced by Ma\~n\'e, establishing existence and uniqueness of equilibrium states for natural classes of potential functions. In particular, we characterize the SRB measures for these diffeomorphisms as unique equilibrium states for a suitable geometric potential. We also obtain large deviations and multifractal results for the unique equilibrium states produced by the main theorem.

Cite

@article{arxiv.1703.05722,
  title  = {Equilibrium states for Ma\~n\'e diffeomorphisms},
  author = {V. Climenhaga and T. Fisher and D. J. Thompson},
  journal= {arXiv preprint arXiv:1703.05722},
  year   = {2017}
}

Comments

This work develops material that originally appeared in the first version of arxiv:1505.06371, originally titled 'Unique equilibrium states for the robustly transitive diffeomorphisms of Ma\~n\'e and Bonatti-Viana'. We split this material into two papers: arxiv:1505.06371 now treats the Bonatti-Viana class and general estimates; this article studies the Ma\~n\'e class. 28 pages, 1 figure

R2 v1 2026-06-22T18:47:59.077Z