J-Ch Yoccoz
Diophantine approximation and dynamics
Abstract:
Lecture 1: Baby model: rotation of a circle; Euclidean algorithm as a
renormalisation procedure; moduli space of flat tori; geodesic flow on the
modular curve. True story: interval exchange transformations; Rauzy induction
as a renormalisation procedure; moduli space of Abelian differentials;
Teichmüller geodesic flow. Lecture 2: Interval exchange transformations satisfying a Roth type
diophantine condition ; the cocycle equation associated to interval exchange
transformations.
