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

26 27

Decomposition results in rational dynamics

By Mikhail Hlushchanka

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.

Information about the video

Date of recording 24/09/2021
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.19812403
Cite this video 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

Domain(s)

Dynamical Systems

Bibliography

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

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