GT ADG-Systèmes DynamiquesQuasi-periodic dynamics in complex dimension one
Davoud Cheraghi (Imperial college, Londres)
Tuesday 23 January 2018 14:00 - Orléans - Salle de Séminaire
Quasi-periodic dynamics in one complex variable reveals fascinating interplays between complex analysis and Diophantine approximations. The question of whether a quasi-periodic dynamics is conjugate to an irrational rotation (linearization) dates back to more than a century ago, with remarkable contributions by C. Siegel, A. Brjuno, and J.-C. Yoccoz. In contrast to the linearisable case, the local dynamics near non-linearizable maps is very complicated. Indeed, there is not a single example of a non-learizable map whose dynamics is completely understood. There have been major recent advances on this problem which have lead to a complete description of the topological behaviour of typical orbits. This is an introductory talk to demonstrate some of these results.