CIRM - Videos & books Library - Renormalization in complex dynamics

Virtualconference

Authors : Shishikura, Mitsuhiro (Author of the conference)
CIRM (Publisher )

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Abstract : We discuss the idea of renormalization for complex dynamical systems. There various types of renormalizations defined via a first return map, appear in complex dynamics, for unimodal maps, homeomorphisms of circle, and germs of irrationally indifferent fixed points of holomorphic maps. The target of renormalization is usually tame and fragile dynamics and the connecting maps are often expanding maps and the exding property helps us to understand the rigid nature of the target maps. We propose the idea of dynamical charts for irrationally indifferent fixed points, in order to reconstruct the original map from the sequence of renormalizations.

Keywords : Renormalization; complex dynamics; rigidity

MSC Codes :
30-XX - Functions of a complex variable, {For analysis on manifolds, See 58-XX}
37-XX - dynamical system - ergodic theory
39-XX - Finite differences and functional equations

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2021-09-21_Shishikura.mp4

Information on the Event

Event Title : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe
Event Organizers : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk
Dates : 20/09/2021 - 24/09/2021
Event Year : 2021
Event URL : https://conferences.cirm-math.fr/2546.html

Citation Data

DOI : 10.24350/CIRM.V.19818203
Cite this video as: Shishikura, Mitsuhiro (2021). Renormalization in complex dynamics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19818203
URI : http://dx.doi.org/10.24350/CIRM.V.19818203

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Bibliography

INOU, Hiroyuki et SHISHIKURA, Mitsuhiro. The renormalization for parabolic fixed points and their perturbation. preprint, 2006. - https://www.math.kyoto-u.ac.jp/~mitsu/pararenorm/ParabolicRenormalization.pdf

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