Robust Transitivity for Endomorphisms

Details Robust Transitivity for Endomorphisms Robust Transitivity for Endomorphisms

2012-01-23

arxiv.org/abs/1201.4806v2

Mathematics

Dynamical Systems

32 pages, 13 figures

Scientific paper

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.

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