Uniqueness of u-Gibbs measures for hyperbolic skew products on \mathbbT⁴

2022/09/19 by Crovisier, Sylvain, Obata, Davi, Poletti, Mauricio
#37C05 #37C40 #37C86 #37D20 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.09151

Abstract

We study the u-Gibbs measures of a certain class of uniformly hyperbolic skew products on \mathbbT⁴. These systems have a strong unstable and a weak unstable directions. We show that C^r-dense and C²-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.

Related

• Open sets of partially hyperbolic skew products having a unique SRB measure
• U-Gibbs measure rigidity for partially hyperbolic endomorphisms on surfaces
• Entropy rigidity of u-Gibbs measures
• Periodic points and measures for a class of skew products
• Bernoulli property for certain skew products over hyperbolic systems