Quantitative Global-Local Mixing for Accessible Skew Products

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 behavior” 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.

Entropy dimension for deterministic walks in random sceneries

Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of irrational rotations with Bernoulli systems, which can be viewed as deterministic walks in random sceneries, and show that this class of models can have any given entropy dimension by choosing suitable rotations for the base system.