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Robust transitivity for endomorphisms
Published online by Cambridge University Press: 06 August 2012
Abstract
We 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.
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- Copyright © 2012 Cambridge University Press
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