Renormalization of analytic maps of the annulus and applications to conjugacy problems

by Prof. Michael Yampolsky (Univ. of Toronto)

Thursday 16 Mar 2023, 13:30 → 15:30 Europe/Rome

CRM - SNS

In a recent series of works with N. Goncharuk, we have constructed an analytic renormalization operator acting on conformal maps of the annulus. We showed that this operator has a hyperbolic horseshoe attractor consisting of Brjuno rotations. I will discuss the resulting renormalization picture and some consequences, including a new proof of Risler’s theorem, and results on smoothness of Arnold tongues.