Stable topological transitivity properties of â,, n -extensions of hyperbolic transformations

Stable topological transitivity properties of â,, n -extensions of hyperbolic transformations

Abstract We consider â,, n skew-products of a class of hyperbolic dynamical systems. It was proved by Nitica and Pollicott [Transitivity of Euclidean extensions of Anosov diffeomorphisms. Ergod. Th. & Dynam. Sys. 25 (2005), 257-269] that for an Anosov diffeomorphism [varphi] of an infranilmanifo...

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Veröffentlicht in:Ergodic theory and dynamical systems 2012-08, Vol.32 (4), p.1435
Hauptverfasser: MOSS, A, WALKDEN, C P
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description Abstract We consider â,, n skew-products of a class of hyperbolic dynamical systems. It was proved by Nitica and Pollicott [Transitivity of Euclidean extensions of Anosov diffeomorphisms. Ergod. Th. & Dynam. Sys. 25 (2005), 257-269] that for an Anosov diffeomorphism [varphi] of an infranilmanifold Λ there is (subject to avoiding natural obstructions) an open and dense set f:Λ[arrow right]â,, N for which the skew-product [varphi] f (x,v)=([varphi](x),v+f(x)) on Λ×â,, N has a dense orbit. We prove a similar result in the context of an Axiom A hyperbolic flow on an attractor. [PUBLICATION ABSTRACT]
doi_str_mv 10.1017/S0143385711000228
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Topology
title Stable topological transitivity properties of â,, n -extensions of hyperbolic transformations
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