Andrew Torok (University of Houston)

Stable ergodicity of smooth compact Lie group extensions of hyperbolic basic sets

Abstract. We obtain sharp results for the genericity and stability of transitivity, ergodicity and mixing for compact connected Lie group extensions over the basic set of a C^s diffeomorphism, $s \geq 2$. In contrast to previous work, our results hold for general hyperbolic basic sets and are valid in the C^r topology for all $r\in(0,s]$ (except that C¹ is replaced by Lipschitz).

Using our results we obtain stable transitivity for (non-compact) $\mathbb{R} ^m$-extensions over a general basic set, thereby generalizing a result of Nitica & Pollicott. We also obtain results on stability of weak mixing for hyperbolic suspension flows and Axiom A flows.

This is joint work with M. Field and I. Melbourne.