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Audiovisual Mathematics Library

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Authors : Thurston, Dylan (Author of the conference)
CIRM (Publisher )

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Abstract : We can conveniently represent post-critically finite topological branched selfcovers of the sphere to itself using maps of graphs. With this representation, there is also a positive characterization of hyperbolic rational maps among these topological branched self-covers, using energies that control elastic 'stretchiness'. In broad terms, a map is rational iff a network of elastic bands gets looser and looser as you pull it back. This complements the older negative characterization of W. Thurston.

Keywords : complex dynamics; extremal length; elastic networks; hyperbolic rational maps; Thurston obstruction; embedding energy; quasiconformal surgery

MSC Codes :
37E25 37E30 - Homeomorphisms and diffeomorphisms of planes and surfaces
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2021-09-21_Thurston.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.19815703
Cite this video as: Thurston, Dylan (2021). Characterizing rational maps positively using graphs . CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19815703
URI : http://dx.doi.org/10.24350/CIRM.V.19815703

See Also

[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.
[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.
[Virtualconference] The visual sphere of an expanding Thurston map / Author of the conference Bonk, Mario.
[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

THURSTON, Dylan P. A positive characterization of rational maps. Annals of Mathematics, 2020, vol. 192, no 1, p. 1-46. - https://doi.org/10.4007/annals.2020.192.1.1

THURSTON, Dylan P. From rubber bands to rational maps: a research report. Research in the Mathematical Sciences, 2016, vol. 3, no 1, p. 1-49. - https://doi.org/10.1186/s40687-015-0039-4

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