Decomposition results in rational dynamics | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Decomposition results in rational dynamics

De Mikhail Hlushchanka

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

There are various classical and more recent decomposition results in mapping class group theory, geometric group theory, and complex dynamics (which include celebrated results by Bill Thurston). We will discuss several natural decompositions that arise in the study of rational maps, such as Pilgrim's canonical decomposition and Levy decomposition (by Bartholdi and Dudko). I will also introduce a new decomposition of rational maps based on the topology of their Julia sets (obtained jointly with Dima Dudko and Dierk Schleicher). At the end of the talk, we will briefly consider connections of this novel decomposition to geometric group theory and self-similar groups.

Informations sur la vidéo

Date de captation 24/09/2021
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.19812403
Citer cette vidéo Hlushchanka, Mikhail (24/09/2021). Decomposition results in rational dynamics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19812403
URL https://dx.doi.org/10.24350/CIRM.V.19812403

Domaine(s)

Systèmes dynamiques

Bibliographie

BARTHOLDI, Laurent et DUDKO, Dzmitry. Algorithmic aspects of branched coverings IV/V. Expanding maps. Transactions of the American Mathematical Society, 2018, vol. 370, no 11, p. 7679-7714. - http://dx.doi.org/10.1090/tran/7199
DOUADY, Adrien et HUBBARD, John H. A proof of Thurston's topological characterization of rational functions. Acta Mathematica, 1993, vol. 171, no 2, p. 263-297. - https://projecteuclid.org/journalArticle/Download?urlid=10.1007%2FBF02392534
DUDKO, Dzmitry et HLUSHCHANKA, Mikhail et SCHLEICHER, Dierk. A canonical decomposition of postcritically finite rational maps. Preprint. - https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxtaWtoYWlsaGx1c2hjaGFua2F8Z3g6MzJjMzdiNjI0MmY5YzdlYg
PILGRIM, Kevin M. Canonical Thurston obstructions. Advances in Mathematics, 2001, vol. 158, no 2, p. 154-168. - https://doi.org/10.1006/aima.2000.1971
SELINGER, Nikita. Thurston's pullback map on the augmented Teichmüller space and applications. Inventiones mathematicae, 2012, vol. 189, no 1, p. 111-142. - http://dx.doi.org/10.1007/s00222-011-0362-3

Codes MSC

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2024

Donner son avis