Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Quasi-periodic dynamics in complex dimension one

Dr. Davoud Cheragi talk

**Date:** 29.04.19 **Time:** 14.00 - 15.00 **Room:** ETH HG G 43

Quasi-periodic dynamics in one complex variable reveals fascinating interplay between complex analysis and Diophantine approximations. The question of whether a nonlinear perturbation of a linear rotation is conjugate to a linear rotation (linearisation) dates back to more than a century ago, with remarkable contributions by C. Siegel, A. Brjuno, and J.-C. Yoccoz. The behaviour of non-linearisable maps is very complicated. Indeed, there is not a single example of a non-linearisable map whose local behaviour is completely understood. There is major recent advances on this problem which has lead to a complete description of the topological behaviour of typical orbits. This is an introductory talk to demonstrate some of these results.