Robust transitivity for endomorphisms

Abstract

AbstractWe address the problem of the conditions under which an endomorphism having a dense orbit is such that a sufficiently close perturbed map also exhibits a dense orbit. For this purpose we give sufficient conditions, covering a large class of examples, for endomorphisms on the $n$-dimensional torus to be robustly transitive: the endomorphism must be volume expanding and any large connected arc must contain a point such that its future orbit belongs to an expanding region.