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

4 27

Quadratic polynomials

By Laurent Bartholdi

Quadratic polynomials have been investigated since the beginnings of complex dynamics, and are often approached through combinatorial theories such as laminations or Hubbard trees. I will explain how both of these approaches fit in a more algebraic framework: that of iterated monodromy groups. The invariant associated with a quadratic polynomial is a group acting on the infinite binary tree, these groups are interesting in their own right, and provide insight and structure to complex dynamics: I will explain in particular how the conversion between Hubbard trees and external angles amounts to a change of basis, how the limbs and wakes may be defined in the language of group theory, and present a model of the Mandelbrot set consisting of groups. This is joint work with Dzmitry Dudko and Volodymyr Nekrashevych.

Information about the video

Date of recording 21/09/2021
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.19810303
Cite this video Bartholdi, Laurent (21/09/2021). Quadratic polynomials. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19810303
URL https://dx.doi.org/10.24350/CIRM.V.19810303

Domain(s)

Bibliography

BARTHOLDI, Laurent et NEKRASHEVYCH, Volodymyr V. Iterated monodromy groups of quadratic polynomials, I. Groups, Geometry, and Dynamics, 2008, vol. 2, no 3, p. 309-336. - https://doi.org/10.4171/GGD/42

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