Paper

Equilibrium states for certain partially hyperbolic attractors*

and

Published 29 May 2020 • © 2020 IOP Publishing Ltd & London Mathematical Society
, , Citation Todd Fisher and Krerley Oliveira 2020 Nonlinearity 33 3409 DOI 10.1088/1361-6544/ab8021

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Author e-mails

tfisher@mathematics.byu.edu

krerley@gmail.com

Author affiliations

1 Department of Mathematics, Brigham Young University, Provo, UT 84602, United States of America

2 Instituto de Matemática, UFAL 57072-090 Maceió, AL, Brazil

Author notes

3 Author to whom any correspondence should be addressed.

Dates

  1. Received 25 September 2019
  2. Revised 4 March 2020
  3. Accepted 16 March 2020
  4. Published

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Abstract

We prove that a class of partially hyperbolic attractors introduced by Castro and Nascimento have unique equilibrium states for natural classes of potentials. We also show if the attractors are C2 and have invariant stable and centre-unstable foliations, then there is a unique equilibrium state for the geometric potential and its 1-parameter family. We do this by applying general techniques developed by Climenhaga and Thompson.

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Footnotes

  • * 

10.1088/1361-6544/ab8021