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Robust transitivity for endomorphisms

Published online by Cambridge University Press:  06 August 2012

CRISTINA LIZANA  and
ENRIQUE PUJALS
CRISTINA LIZANA
Affiliation:
Departamento de Matemática, Facultad de Ciencias, Universidad de Los Andes, La Hechicera-Mérida, 5101, Venezuela (email: [email protected])
ENRIQUE PUJALS
Affiliation:
IMPA, Estrada Dona Castorina 110, CEP 22460-320 Rio de Janeiro, Brazil (email: [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 4 , August 2013 , pp. 1082 - 1114
Copyright
Copyright © 2012 Cambridge University Press 

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