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

3 27

Docile transcendental entire functions

By James Waterman

holomorphic dynamics, transcendental entire function, docile

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.

Information about the video

Date of recording 20/09/2021
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.19815903
Cite this video Waterman, James (20/09/2021). Docile transcendental entire functions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19815903
URL https://dx.doi.org/10.24350/CIRM.V.19815903

Domain(s)

Dynamical Systems

MSC codes

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