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Audiovisual Mathematics Library

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Authors : Martí-Pete, David (Author of the conference)
CIRM (Publisher )

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Abstract : We construct a transcendental entire function for which infinitely many Fatou components share the same boundary. This solves the long-standing open problem whether Lakes of Wada continua can arise in complex dynamics, and answers the analogue of a question of Fatou from 1920 concerning Fatou components of rational functions. Our theorem also provides the first example of an entire function having a simply connected Fatou component whose closure has a disconnected complement, answering a recent question of Boc Thaler. Using the same techniques, we give new counterexamples to a conjecture of Eremenko concerning curves in the escaping set of an entire function. This is joint work with Lasse Rempe and James Waterman.

Keywords : lakes of Wada; transcendental dynamics; complex dynamics; wandering domains; entire functions; approximation

MSC Codes :
30D05 - Functional equations in the complex domain, iteration and composition of analytic functions
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
54F15 - Continua and generalizations
37B45 - Continua theory in dynamics

Information on the Video

Film maker :

Hennenfent, Guillaume

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Download :

https://videos.cirm-math.fr/2021-09-20_Marti-Piete.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.19813503
Cite this video as: Martí-Pete, David (2021). Wandering lakes of Wada. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19813503
URI : http://dx.doi.org/10.24350/CIRM.V.19813503

See Also

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Bibliography

MARTÍ-PETE, David, REMPE, Lasse, et WATERMAN, James. Wandering Lakes of Wada. arXiv preprint arXiv:2108.10256, 2021. - https://arxiv.org/abs/2108.10256

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