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 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]