Robust Transitivity for Endomorphisms

2012/01/23 by Lizana, Cristina, Pujals, Enrique · 1 citation
#37B05 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.4806

Abstract

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.

Cited by

• Robustly transitive maps with critical points and large dimensional central spaces

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