Orateur
Description
In this talk, I will discuss a well-known renormalization technique for the first return map of foliations on surfaces, known as Rauzy-Veech induction.
A key result in this setting is the exponential tail property of the renormalization process.
It was established by Avila-Gouezël-Yoccoz in the case of interval exchange maps (associated to orientable foliations on orientable surfaces) and later by Avila-Resende for linear involutions (emerging from non-orientable foliations).
These results have significant implications for the dynamics of the Teichmüller flow and were instrumental in proving a spectral gap property.
After providing an overview of these techniques, I will explain some other strong consequences and discuss the non-orientable cases as appearing for instance in tiling billiards.
