This week's seminars
Pure Maths Colloquium: Quasi-periodic dynamics in complex dimension one
9 December 2019 13:00 in CM101
Quasi-periodic dynamics in one complex variable reveals fascinating interplays between geometric 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 made by C. L. Siegel, A. D. 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 dynamical behaviour is completely understood. There has been recent significant advances on this problem using renormalisation methods. This is an introductory talk to present some of these results.
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