Piecewise affine homeomorphisms of the circle and dilation surfaces

Data Seminario: 
06-May-2021
Ora Inizio: 
16:00
Ora Fine: 
17:00
Selim Ghazouani
Université d’Orsay, France

In this talk I will consider the following question: if one picks a piecewise affine map of the circle “at random”, what dynamical behaviour are we likely to observe? The case of standard circle diffeomorphisms has been studied by Herman in the 80s; in this emblematic case the problem can be reduced to theorems close to KAM theory. For the piecewise affine case, we put forward a geometric approach, inspired by methods from both Teichmüller theory and hyperbolic geometry.