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Audiovisual Mathematics Library

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Multi angle

Authors : Bartholdi, Laurent (Author of the conference)
CIRM (Publisher )

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Abstract : 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.

Keywords : Complex dynamics; self-similar groups; laminations; external angles; Hubbard trees

MSC Codes :
20E08 - Groups acting on trees
37B10 - Symbolic dynamics
37C25 - Fixed points, periodic points, fixed-point index theory
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F45

Information on the Video

Film maker :

Hennenfent, Guillaume

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Download :

https://videos.cirm-math.fr/2021-09-21_Bartholdi.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.19810303
Cite this video as: Bartholdi, Laurent (2021). Quadratic polynomials. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19810303
URI : http://dx.doi.org/10.24350/CIRM.V.19810303

See Also

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[Virtualconference] Entire functions with Cantor bouquet Julia sets / Author of the conference Pardo-Simon, Leticia.
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[Virtualconference] Arithmetic geometric models for the renormalisation of irrationally indifferent attractors / Author of the conference Cheraghi, Davoud.
[Virtualconference] Tips of tongues in the double standard family / Author of the conference Buff, Xavier.
[Multi angle] Eremenko's conjecture, Devaney's hairs, and the growth of counterexamples / Author of the conference Brown, Andrew.
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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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