Henk Bruin (Vienna): Regular variations for almost Anosov diffeomorphisms. (Joint work with Dalia Terhesiu)

Abstract: The current operator renewal-type approach to obtain
polynomial mixing rates in various dynamical systems requires
that the tails of a certain inducing scheme have regular variation.
An almost Anosov diffeomorphism is a diffeomorphism (in our case
on the 2-torus) that satisfies the Anosov properties except at a finite
set of neutral saddle points.
In this invertible setting (which additionally requires the use of a
anisotropic Banach space of distribution similar to the one used before
by Liverani & Terhesiu), the regular variation of the tails has been
treated only in very specific settings and/or with unsatisfactory estimates.
In this talk I want to present a new method which works
in much greater generality and gives much more precise estimates.