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Complex Rotation Numbers and Renormalization

[HYBRID WORKSHOP] Connections Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables February 02, 2022 - February 04, 2022

February 03, 2022 (10:40 AM PST - 11:05 AM PST)
Speaker(s): Nataliia Goncharuk (University of Toronto, Mississauga)
Location: SLMath: Online/Virtual
Tags/Keywords

  • rotation numbers

  • fractals

  • renormalization operator

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

Complex Rotation Numbers And Renormalization
Abstract

The complex rotation number is an invariant related to the dynamics of an analytic circle diffeomorphism f. It produces a nice fractal set ``bubbles'' analogous to Arnold's tongues. I will explain how the renormalization operator makes the ``bubbles'' self-similar and controls their sizes.
Supplements
92532?type=thumb Complex Rotation Numbers and Renormalization 1.78 MB application/pdf Download
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Complex Rotation Numbers And Renormalization

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