# Renormalization of analytic maps of the annulus and applications to conjugacy problems – Michael Yampolsky (Univ. of Toronto)

CRM – SNS.

#### Abstract

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.

Further information is available on the event page on the Indico platform.

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