Uniqueness of equilibrium states for some partially hyperbolic horseshoes (Q765037)

In this paper, the existence and uniqueness of equilibrium states are considered for non-uniformly hyperbolic (invertible) systems. Recently, \textit{J. Buzzi} et al. [Ergodic Theory Dyn. Syst. 32, No. 1, 63--79 (2012; Zbl 1257.37023)] obtained a method to prove uniqueness of maximal entropy measures for certain partially hyperbolic systems which are derived from Anosov systems. The authors consider a partially hyperbolic horseshoe, that was first constructed and studied by \textit{L. Díaz} et al. in [Ergodic Theory Dyn. Syst. 29, No. 2, 433--474 (2009; Zbl 1160.37328)], and prove the uniqueness of equilibrium states for a class of potentials. In particular, the existence of a unique maximal entropy measure is proven for the horseshoe.