English
The visual sphere of an expanding Thurston map
Virtualconference
Auteurs : Bonk, Mario (Auteur de la Conférence)
CIRM (Editeur )
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
CIRM (Editeur )
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Résumé :
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
Codes MSC : Keywords : Expanding Thurston map; visual metric; conformal dimension
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
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 02/11/2021 Date de captation : 23/09/2021 Sous collection : Research School arXiv category : Dynamical Systems ; Complex Variables Domaine : Analysis and its Applications ; Geometry Format : MP4 (.mp4) - HD Durée : 01:06:58 Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-23_Bonk.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexeOrganisateurs de la rencontre : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk Dates : 20/09/2021 - 24/09/2021 Année de la rencontre : 2021 URL Congrès : https://conferences.cirm-math.fr/2546.html
Données de citation
DOI : 10.24350/CIRM.V.19810903Citer cette vidéo: 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 |
Voir aussi
- [Virtualconference] Renormalization in complex dynamics / Auteur de la Conférence Shishikura, Mitsuhiro.
- [Multi angle] Characterizing Thurston maps by lifting trees / Auteur de la Conférence Winarski, Rebecca.
- [Multi angle] Docile transcendental entire functions / Auteur de la Conférence Waterman, James.
- [Virtualconference] Characterizing rational maps positively using graphs / Auteur de la Conférence Thurston, Dylan.
- [Multi angle] Transcendental Thurston Theory for entire functions and compositions / Auteur de la Conférence Shemyakov, Sergey.
- [Multi angle] Iterated monodromy groups and transcendental dynamics / Auteur de la Conférence Reinke, Bernhard.
- [Multi angle] A dynamical homeomorphism between the Mandelbrot set $M$ and the parabolic Mandelbrot set $M_{1}$ / Auteur de la Conférence Petersen, Carsten Lunde.
- [Virtualconference] Entire functions with Cantor bouquet Julia sets / Auteur de la Conférence Pardo-Simon, Leticia.
- [Multi angle] Contracting self-similar groups and conformal dimension / Auteur de la Conférence Nekrashevych, Volodymyr.
- [Virtualconference] Interbreeding in conformal dynamics, and its applications near and far / Auteur de la Conférence Mukherjee, Sabyasachi.
- [Multi angle] Wandering lakes of Wada / Auteur de la Conférence Martí-Pete, David.
- [Multi angle] Story of the Feigenbaum point / Auteur de la Conférence Lyubich, Mikhail.
- [Multi angle] Transcendental Julia sets of minimal Hausdorff dimension / Auteur de la Conférence Lazebnik, Kirill.
- [Multi angle] Introduction to Thurston's theorems / Auteur de la Conférence Hubbard, John H..
- [Multi angle] Decomposition results in rational dynamics / Auteur de la Conférence Hlushchanka, Mikhail.
- [Multi angle] Meromorphic maps of finite type: parameter space / Auteur de la Conférence Fagella, Nuria.
- [Multi angle] Hyperbolicity of renormalization for bi-cubic circle maps with bounded combinatorics / Auteur de la Conférence Estevez Jacinto, Gabriela Alexandra.
- [Virtualconference] Near-degenerate regime in neutral renormalization / Auteur de la Conférence Dudko, Dzmitry.
- [Multi angle] Box renormalization as a 'black box' / Auteur de la Conférence Drach, Kostiantyn.
- [Virtualconference] Arithmetic geometric models for the renormalisation of irrationally indifferent attractors / Auteur de la Conférence Cheraghi, Davoud.
- [Virtualconference] Tips of tongues in the double standard family / Auteur de la Conférence Buff, Xavier.
- [Multi angle] Eremenko's conjecture, Devaney's hairs, and the growth of counterexamples / Auteur de la Conférence Brown, Andrew.
- [Multi angle] Transcendental dynamics and infinite-dimensional Thurston theory / Auteur de la Conférence Bogdanov, Konstantin.
- [Virtualconference] Transcendental functions with small singular sets / Auteur de la Conférence Bishop, Christopher.
- [Multi angle] Polynomial versus transcendental dynamics / Auteur de la Conférence Benini, Anna Miriam.
- [Multi angle] Quadratic polynomials / Auteur de la Conférence Bartholdi, Laurent.
Bibliographie
- BONK, Mario et MEYER, Daniel. Expanding thurston maps. American Mathematical Soc., 2017. - https://doi.org/10.1090/surv/225
