Stable topological transitivity properties of Rn-extensions of hyperbolic transformations

2011 We consider Rn skew-products of a class of hyperbolic dynamical systems. It was proved by Niţica ̆ and Pollicott [NP] that for an Anosov diffeomorphism φ of an infranilmanifold Λ there is (subject avoiding natural obstructions) an open and dense set f: Λ → RN for which the skew-product φf (x, s) = (φ(x), s+ 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.