Stable topological transitivity properties of ℝn-extensions of hyperbolic transformations

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.