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DTSTART:20220124T160000Z
DTEND:20220124T170000Z
SUMMARY:Colloquium - Nataliya Goncharuk
DESCRIPTION:

** Title: **Complex rotation numbers and renormalization

** Abstract: ** The complex rotation number (suggested by V.Arnold) is an invariant related to the dynamics of an analytic circle diffeomorphism f. Complex rotation numbers give rise to a nice fractal set ``bubbles'' analogous to classical Arnold's tongues.

I will give a survey on complex rotation numbers and list open problems. Also\, I will explain how the renormalization operator makes the ``bubbles'' self-similar and controls their sizes.
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