Stable topological transitivity properties of R n-extensions of hyperbolic transformations

We consider n skew-products of a class of hyperbolic dynamical systems. It was proved by Ni and Pollicott [Transitivity of Euclidean extensions of Anosov diffeomorphisms. Ergod. Th. & Dynam. Sys. 25 (2005), 257-269] that for an Anosov diffeomorphism ø of an infranilmanifold there is (subject to avoiding natural obstructions) an open and dense set f: n for which the skew-product ø f(x,v)=(ø(x),v+f(x)) on á - n has a dense orbit. We prove a similar result in the context of an Axiom A hyperbolic flow on an attractor. © Copyright Cambridge University Press 2011.