Quantitative global-local mixing for accessible skew products

Abstract: Skew products, or group extensions, over hyperbolic diffeomorphisms are important examples of partially hyperbolic systems. Dolgopyat showed that generic compact extensions of topologically mixing Axiom A diffeomorphisms are rapidly mixing, namely the decay of correlations of smooth observables is faster than any given polynomial. In this talk, we will consider the case of $\mathbb{R}$-extensions. We will focus on global-local mixing, one of the possible notions of mixing for infinite measure preserving systems. We will present a quantitative mixing result for skew products which satisfy an accessibility condition; in particular, we will relate the rate of decay of correlations to the ''low frequency behaviour'' of the spectral measure associated to our global observables. This is a joint work with Paolo Giulietti and Andy Hammerlindl.

dynamical systems

Audience: researchers in the topic

Sydney Dynamics Group Seminar

Series comments: Description: Research seminar for dynamical systems topics