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Stable topological transitivity properties of ℝn-extensions of hyperbolic transformations

Published online by Cambridge University Press:  13 June 2011

A. MOSS  and
C. P. WALKDEN
A. MOSS
Affiliation:
School of Mathematics, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK (email: [email protected], [email protected])
C. P. WALKDEN
Affiliation:
School of Mathematics, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK (email: [email protected], [email protected])
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Abstract

We consider ℝn skew-products of a class of hyperbolic dynamical systems. It was proved by Niţică and Pollicott [Transitivity of Euclidean extensions of Anosov diffeomorphisms. Ergod. Th. & Dynam. Sys. 25 (2005), 257–269] that for an Anosov diffeomorphism ϕ of an infranilmanifold Λ there is (subject to avoiding natural obstructions) an open and dense set f:Λ→ℝN for which the skew-product ϕf(x,v)=(ϕ(x),v+f(x)) on Λ×ℝN has a dense orbit. We prove a similar result in the context of an Axiom A hyperbolic flow on an attractor.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 4 , August 2012 , pp. 1435 - 1443
Copyright
Copyright © Cambridge University Press 2011

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