Colloquium - Nataliya Goncharuk

Date: January 24, 2022

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Nataliya Goncharuk, University of Toronto, Canada

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.