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Complex Rotation Numbers and Renormalization

Adventurous Berkeley Complex Dynamics May 02, 2022 - May 06, 2022

May 02, 2022 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Nataliia Goncharuk (University of Toronto, Mississauga)
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Complex Rotation Numbers And Renormalization


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.

93180?type=thumb Complex Rotation Numbers and Renormalization 2.24 MB application/pdf Download
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Complex Rotation Numbers And Renormalization

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