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Audiovisual Mathematics Library

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Virtualconference

Authors : Bonk, Mario (Author of the conference)
CIRM (Publisher )

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Abstract : Every expanding Thurston map gives rise to a fractal geometry on its underlying 2-sphere. Many dynamical properties of the map are encoded in this fractal, called the 'visual sphere' of the map. An interesting question is how to determine the (Ahlfors regular) conformal dimension of the visual sphere if the map is obstructed. In my talk I will give an introduction to this subject and discuss some recent progress.

Keywords : Expanding Thurston map; visual metric; conformal dimension

MSC Codes :
30D05 - Functional equations in the complex domain, iteration and composition of analytic functions
37-02 - research exposition
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F20 - Combinatorics and topology in relation with holomorphic dynamical systems
30L10 - Quasiconformal mappings in metric spaces

Information on the Video

Film maker :

Hennenfent, Guillaume

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https://videos.cirm-math.fr/2021-09-23_Bonk.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.19810903
Cite this video as: Bonk, Mario (2021). The visual sphere of an expanding Thurston map. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19810903
URI : http://dx.doi.org/10.24350/CIRM.V.19810903

See Also

[Virtualconference] Renormalization in complex dynamics / Author of the conference Shishikura, Mitsuhiro.
[Multi angle] Characterizing Thurston maps by lifting trees / Author of the conference Winarski, Rebecca.
[Multi angle] Docile transcendental entire functions / Author of the conference Waterman, James.
[Virtualconference] Characterizing rational maps positively using graphs / Author of the conference Thurston, Dylan.
[Multi angle] Transcendental Thurston Theory for entire functions and compositions / Author of the conference Shemyakov, Sergey.
[Multi angle] Iterated monodromy groups and transcendental dynamics / Author of the conference Reinke, Bernhard.
[Multi angle] A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$ / Author of the conference Petersen, Carsten Lunde.
[Virtualconference] Entire functions with Cantor bouquet Julia sets / Author of the conference Pardo-Simon, Leticia.
[Multi angle] Contracting self-similar groups and conformal dimension / Author of the conference Nekrashevych, Volodymyr.
[Virtualconference] Interbreeding in conformal dynamics, and its applications near and far / Author of the conference Mukherjee, Sabyasachi.
[Multi angle] Wandering lakes of Wada / Author of the conference Martí-Pete, David.
[Multi angle] Story of the Feigenbaum point / Author of the conference Lyubich, Mikhail.
[Multi angle] Transcendental Julia sets of minimal Hausdorff dimension / Author of the conference Lazebnik, Kirill.
[Multi angle] Introduction to Thurston's theorems / Author of the conference Hubbard, John H..
[Multi angle] Decomposition results in rational dynamics / Author of the conference Hlushchanka, Mikhail.
[Multi angle] Meromorphic maps of finite type: parameter space / Author of the conference Fagella, Nuria.
[Multi angle] Hyperbolicity of renormalization for bi-cubic circle maps with bounded combinatorics / Author of the conference Estevez Jacinto, Gabriela Alexandra.
[Virtualconference] Near-degenerate regime in neutral renormalization / Author of the conference Dudko, Dzmitry.
[Multi angle] Box renormalization as a 'black box' / Author of the conference Drach, Kostiantyn.
[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.
[Multi angle] Transcendental dynamics and infinite-dimensional Thurston theory / Author of the conference Bogdanov, Konstantin.
[Virtualconference] Transcendental functions with small singular sets / Author of the conference Bishop, Christopher.
[Multi angle] Polynomial versus transcendental dynamics / Author of the conference Benini, Anna Miriam.
[Multi angle] Quadratic polynomials / Author of the conference Bartholdi, Laurent.

Bibliography

BONK, Mario et MEYER, Daniel. Expanding thurston maps. American Mathematical Soc., 2017. - https://doi.org/10.1090/surv/225

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