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Quadratic polynomials

De Laurent Bartholdi

Apparaît dans la collection : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

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.

Informations sur la vidéo

Date de captation 21/09/2021
Date de publication 02/11/2021
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19810303
Citer cette vidéo 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

Domaine(s)

Bibliographie

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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