Quadratic polynomials | Vidéo | Carmin.tv

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Quadratic polynomials

By Laurent Bartholdi

Appears in 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.

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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