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Transitivity of Euclidean extensions of Anosov diffeomorphisms

Published online by Cambridge University Press:  22 December 2004

VIOREL NIŢICĂ
Affiliation:
Department of Mathematics, West Chester University of Pennsylvania, West Chester, PA 19383, USA and Institute of Mathematics of the Romanian Academy, PO Box 1–764, RO-70700 Bucharest, Romania (e-mail: VNITICA@wcupa.edu)
MARK POLLICOTT
Affiliation:
Department of Mathematics, Manchester University, Oxford Road, Manchester, M13 9PL, UK (e-mail: mp@ma.man.ac.uk)

Abstract

We consider the class of $\mathbb{R}^n$ extensions of Anosov diffeomorphisms on infranilmanifolds, and find necessary and sufficient conditions for topological transitivity. In particular, if the fiber is $\mathbb{R}$, the existence of a semi-orbit with the projection on $\mathbb{R}$ unbounded from above and from below is equivalent to topological transitivity. We also show that in the above class topological transitivity and stable topological transitivity are equivalent.

Type
Research Article
Copyright
2004 Cambridge University Press

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