Robust transitivity for endomorphisms

2012 Ergodic Theory and Dynamical Systems  
We address the problem about under what conditions an endomorphism having a dense orbit, verifies that a sufficiently close perturbed map also exhibits a dense orbit. In this direction, we give sufficient conditions, that cover 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 belong to an expanding region.
doi:10.1017/s0143385712000247 fatcat:xvndyj3bkvbufi4y6fyk5hreiy