Speaker
Corinna Ulcigrai, ETH Zürich
Abstract
Circle rotations and circle diffeomorphisms can be seen as Poincare maps of flows on tori. The maps that arise when considering Poincare maps of smooth flows on higher genus surfaces are piecewise continuous diffeomorphisms, known as generalized interval exchange maps (GIETs).
We will discuss recent progress on linearization and rigidity questions (such as when a generalized IET is conjugated to its linear model or what is the regularity of the conjugacy) for GIETs, explaining the similarities but also the crucial differences with the classical theory of circle diffeos.
We will then discuss C^{1+\alpha) regularity of the conjugacy when exponential convergence of renormalization holds.
The talk is based on joint works with Selim Ghazouani.