Quasi-periodic dynamics in complex dimension one
Analysis and Geometry Seminar
14th February 2019, 3:00 pm – 4:00 pm
Howard House, 4th Floor Seminar Room
Quasi-periodic dynamics in one complex variable reveals fascinating interplays 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.