Maximal measures of diffeomorphisms with circle fiber bundle
In this paper, we study the maximal measures of partially hyperbolic diffeomorphisms whose center bundle is 1- dimensional and forms a circle bundle. We show that for any such C2 diffeomorphism which is accessible, and is not of ‘rotation type’, the maximal measures can be identified by skeleton, a set of finite number of saddles. Moreover, the maximal measure has exponential decay of correlations for Holder observables. This is a joint work with Raul Ures and Marcelo Viana.