English
Renormalization in complex dynamics
Virtualconference
Auteurs : Shishikura, Mitsuhiro (Auteur de la Conférence)
CIRM (Editeur )
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
CIRM (Editeur )
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Résumé :
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
Codes MSC : Keywords : Renormalization; complex dynamics; rigidity
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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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 02/11/2021 Date de captation : 21/09/2021 Sous collection : Research talks arXiv category : Dynamical Systems Domaine : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 01:06:44 Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-21_Shishikura.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexeOrganisateurs de la rencontre : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk Dates : 20/09/2021 - 24/09/2021 Année de la rencontre : 2021 URL Congrès : https://conferences.cirm-math.fr/2546.html
Données de citation
DOI : 10.24350/CIRM.V.19818203Citer cette vidéo: 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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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
