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Docile transcendental entire functions

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Authors : Waterman, James (Author of the conference)
CIRM (Publisher )

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Abstract : Several important problems in complex dynamics are centered around the local connectivity of Julia sets of polynomials and of the Mandelbrot set. Importantly, when the Julia set of a polynomial is locally connected, the topological dynamics ofthe map can be completely described as a quotient of a power map on the circle.Local connectivity of the Julia set is less significant for transcendental entire functions. Nevertheless, by restricting to a class of transcendental entire functions, known as docile functions, we obtain a similar concept by describing the topological dynamics as a quotient of a simpler disjoint-type map. We will discuss the notion ofdocile functions, as well as some of their properties. This is joint work with Lasse Rempe.

Keywords : holomorphic dynamics, transcendental entire function, docile

MSC Codes :
30D05 - Functional equations in the complex domain, iteration and composition of analytic functions
30F20 - Classification theory of Riemann surfaces
30F45 - Conformal metrics (hyperbolic, Poincaré, distance functions)
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 02/11/2021
    Conference Date : 20/09/2021
    Subseries : Research talks
    arXiv category : Dynamical Systems
    Mathematical Area(s) : Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Video Time : 00:29:23
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-09-20_Waterman.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.19815903
Cite this video as: Waterman, James (2021). Docile transcendental entire functions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19815903
URI : http://dx.doi.org/10.24350/CIRM.V.19815903

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