Sydney Dynamics Group: Ravotti -- Quantitative global-local mixing for accessible skew products

Dear all, 

This week, Friday July 3, Davide Ravotti (Monash University) will give a talk at 4pm
(Sydney time) via Zoom.  

Zoom link: https://uni-sydney.zoom.us/j/91246625911 

Meeting ID: 912 4662 5911 

Title: 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.  


Past talks can be found on the YouTube channel:
https://www.youtube.com/channel/UCZqgDJ21wbdzMbeIdealpUg/ 

I hope to see you all online.  

Lachlan