Ian Melbourne (University of Warwick):
Mixing and rates of mixing for infinite measure systems with discrete
and continuous time.
Abstract: A recent paper, joint with Dalia Terhesiu, developed a theory of
mixing and rates of mixing for discrete dynamical systems with an infinite
invariant measure. The method combines operator renewal theory techniques
(Sarig, Gouezel) with probabilistic ideas of Garsia & Lamperti.
In this talk, I will review these results. Also, I will describe some recent
work, again joint with Dalia Terhesiu, where we obtain similar results for
continuous time. The techniques are similar, but the estimates are trickier
than for discrete time and ideas of Dolgopyat are also required.