On the plaque topological stability of partially hyperbolic diffeomorphisms

Abstract

We prove that every dynamically coherent plaque expansive partially hyperbolic diffeomorphism is topologically stable with respect to the central foliation (in short, {\em plaque topologically stable}). Next, we study partially hyperbolic diffeomorphisms that are both expansive and topologically stable with respect to a central foliation. We show that the center chain recurrent set for such diffeomorphisms belongs to the closure of the center periodic points.