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Last update: 23/03/2003

 Houches March 2003

École de physique des Houches

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.

lecture: