Quantitative global-local mixing for accessible skew products
Dynamical Systems
2021-08-24 v2 Mathematical Physics
math.MP
Probability
Abstract
We study global-local mixing for a family of accessible skew products with an exponentially mixing base and non-compact fibers, preserving an infinite measure. For a dense set of almost periodic global observables, we prove rapid mixing; and for a dense set of global observables vanishing at infinity, we prove polynomial mixing. More generally, we relate the speed of mixing to the "low frequency behaviour" of the spectral measure associated to our global observables. Our strategy relies on a careful choice of the spaces of observables and on the study of a family of twisted transfer operators.
Cite
@article{arxiv.2006.06539,
title = {Quantitative global-local mixing for accessible skew products},
author = {P. Giulietti and A. Hammerlindl and D. Ravotti},
journal= {arXiv preprint arXiv:2006.06539},
year = {2021}
}
Comments
To appear in Annales Henri Poincar\'e