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Decomposition results in rational dynamics

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Authors : Hlushchanka, Mikhail (Author of the conference)
CIRM (Publisher )

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Abstract : 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.

Keywords : rational dynamics; Julia sets; invariant graphs; Thurston maps; obstructions; decomposition theory

MSC Codes :
20E08 - Groups acting on trees
20F67 - Hyperbolic groups and nonpositively curved groups
37B10 - Symbolic dynamics
37B40 - Topological entropy
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F20 - Combinatorics and topology in relation with holomorphic dynamical systems

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 02/11/2021
    Conference Date : 24/09/2021
    Subseries : Research School
    arXiv category : Dynamical Systems
    Mathematical Area(s) : Combinatorics ; Dynamical Systems & ODE ; Topology
    Format : MP4 (.mp4) - HD
    Video Time : 00:54:58
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-09-24_Hlushchanka.mp4

Information on the Event

Event Title : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe
Event Organizers : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk
Dates : 20/09/2021 - 24/09/2021
Event Year : 2021
Event URL : https://conferences.cirm-math.fr/2546.html

Citation Data

DOI : 10.24350/CIRM.V.19812403
Cite this video as: Hlushchanka, Mikhail (2021). Decomposition results in rational dynamics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19812403
URI : http://dx.doi.org/10.24350/CIRM.V.19812403

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