Wandering lakes of Wada | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Wandering lakes of Wada

By David Martí-Pete

Appears in collection : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

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.

Information about the video

Date of recording 20/09/2021
Date of publication 02/11/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19813503
Cite this video Martí-Pete, David (20/09/2021). Wandering lakes of Wada. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19813503
URL https://dx.doi.org/10.24350/CIRM.V.19813503

Domain(s)

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

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2024

Give feedback