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

A. Moss, C. P. Walkden

    Research output: Contribution to journalArticlepeer-review

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)1435-1443
    Number of pages8
    JournalErgodic Theory and Dynamical Systems
    Volume32
    Issue number4
    DOIs
    Publication statusPublished - Aug 2012

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