Ergodic properties of partially hyperbolic dynamical systems and weakly rigid systems

Abstract

This research project intends to study the structure of invariant ergodic measures, maximum entropy ergodic measures and the occurrence of the Bernoulli property for partially hyperbolic diffeomorphisms, addressing open problems formulated by the author of this project, by F. Hertz, J. R. Hertz, R. Ures, A. Wilkinson (see problems related to ergodic properties of partially hyperbolic diffeomorphisms), and in the literature by other names of the area such as A. Tahzibi, S. Crovisier and J. Buzzi (see problems related to finiteness of maximum entropy measures) among other.