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Virtualconference

Authors : Dudko, Dzmitry (Author of the conference)
CIRM (Publisher )

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Abstract : A fundamental fact about Riemann surfaces is that they degenerate in a specific pattern — along thin annuli or wide rectangles. As it was demonstrated by W. Thurston in his realization theorem, we can often understand the dynamical system by establishing a priori bounds (a non-escaping property) in the near-degenerate regime. Similar ideas were proven to be successful in the Renormalization Theory of the Mandelbrot set. We will start the talk by discussing a dictionary between Thurston and Renormalization theories. Then we will proceed to neutral renormalization associated with the main cardioid of the Mandelbrot set. We will show how the Transcendental Dynamics naturally appear on the renormalization unstable manifolds. In conclusion, we will describe uniform a priori bounds for neutral renormalization — joint work with Misha Lyubich.

MSC Codes :
37FXX - complex dynamical systems

Information on the Video

Film maker :

Hennenfent, Guillaume

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Download :

https://videos.cirm-math.fr/2021-09-22_Dudko.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.19812003
Cite this video as: Dudko, Dzmitry (2021). Near-degenerate regime in neutral renormalization. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19812003
URI : http://dx.doi.org/10.24350/CIRM.V.19812003

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.
[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

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