Transcendental Julia sets of minimal Hausdorff dimension | Vidéo | Carmin.tv

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Transcendental Julia sets of minimal Hausdorff dimension

By Kirill Lazebnik

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

We show the existence of transcendental entire functions $f: \mathbb{C} \rightarrow \mathbb{C}$ with Hausdorffdimension 1 Julia sets, such that every Fatou component of $f$ has infinite inner connectivity. We also show that there exist singleton complementary components of any Fatou component of $f$, answering a question of Rippon+Stallard. Our proof relies on a quasiconformal-surgery approach. This is joint work with Jack Burkart.

Information about the video

Date of recording 21/09/2021
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.19813003
Cite this video Lazebnik, Kirill (21/09/2021). Transcendental Julia sets of minimal Hausdorff dimension. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19813003
URL https://dx.doi.org/10.24350/CIRM.V.19813003

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Bibliography

BURKART, Jack et LAZEBNIK, Kirill. Transcendental Julia Sets of Minimal Hausdorff Dimension. arXiv preprint arXiv:2109.05001, 2021. - https://arxiv.org/abs/2109.05001

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