Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

Collection Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

Organizer(s) Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk

Date(s) 20/09/2021 - 24/09/2021

linked URL https://conferences.cirm-math.fr/2546.html

00:00:00 / 00:00:00

6 27

Renormalization in complex dynamics

By Mitsuhiro Shishikura

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.

Information about the video

Date of recording 21/09/2021
Date of publication 02/11/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19818203
Cite this video Shishikura, Mitsuhiro (21/09/2021). Renormalization in complex dynamics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19818203
URL https://dx.doi.org/10.24350/CIRM.V.19818203

Domain(s)

Dynamical Systems

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

MSC codes

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