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Renormalization in complex dynamics

De Mitsuhiro Shishikura

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

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.

Informations sur la vidéo

Date de captation 21/09/2021
Date de publication 02/11/2021
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19818203
Citer cette vidéo 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

Domaine(s)

Systèmes dynamiques

Bibliographie

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

Codes MSC

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