Uniqueness of $u$-Gibbs measures for hyperbolic skew products on $\mathbb{T}^4$

Sylvain Crovisier; Davi Obata; Mauricio Poletti

Uniqueness of $u$-Gibbs measures for hyperbolic skew products on $\mathbb{T}^4$

Dynamical Systems 2023-12-07 v2

Authors: Sylvain Crovisier , Davi Obata , Mauricio Poletti

Abstract

We study the $u$ -Gibbs measures of a certain class of uniformly hyperbolic skew products on $\mathbb{T}^4$ . These systems have a strong unstable and a weak unstable directions. We show that $C^r$ -dense and $C^2$ -open in this set every $u$ -Gibbs measure is SRB, in particular, there is only one such measure. As an application of this, we can obtain the minimality of the strong unstable foliation.

Keywords

u-gibbs measures hyperbolic skew products srb measures unstable foliation minimality torus maps

Cite

@article{arxiv.2209.09151,
  title  = {Uniqueness of $u$-Gibbs measures for hyperbolic skew products on $\mathbb{T}^4$},
  author = {Sylvain Crovisier and Davi Obata and Mauricio Poletti},
  journal= {arXiv preprint arXiv:2209.09151},
  year   = {2023}
}

Comments

18 pages, 4 figures

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