Equilibrium states for center isometries

Journal article

Pablo D. Carrasco, Federico Rodriguez-Hertz
Journal of the Institute of Mathematics of Jussieu, First view, 2023, pp. 1--61

DOI: 10.1017/S147474802300018X

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APA Click to copy
Carrasco, P. D., & Rodriguez-Hertz, F. (2023). Equilibrium states for center isometries. Journal of the Institute of Mathematics of Jussieu, First view, 1–61. https://doi.org/10.1017/S147474802300018X

Chicago/Turabian Click to copy
Carrasco, Pablo D., and Federico Rodriguez-Hertz. “Equilibrium States for Center Isometries.” Journal of the Institute of Mathematics of Jussieu First view (2023): 1–61.

MLA Click to copy
Carrasco, Pablo D., and Federico Rodriguez-Hertz. “Equilibrium States for Center Isometries.” Journal of the Institute of Mathematics of Jussieu, vol. First view, 2023, pp. 1–61, doi:10.1017/S147474802300018X.

BibTeX Click to copy

@article{carrasco2023a,
  title = {Equilibrium states for center isometries},
  year = {2023},
  journal = {Journal of the Institute of Mathematics of Jussieu},
  pages = {1--61},
  volume = {First view},
  doi = {10.1017/S147474802300018X},
  author = {Carrasco, Pablo D. and Rodriguez-Hertz, Federico}
}

We develop a geometric method to establish existence and uniqueness of equilibrium states associated to some H\"older potentials for center isometries (as are regular elements of Anosov actions), in particular the entropy maximizing measure and the SRB measure. It is also given a characterization of equilibrium states in terms of their disintegrations along stable and unstable foliations. Finally, we show that the resulting system is isomorphic to a Bernoulli scheme.