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Transcendental Julia sets of minimal Hausdorff dimension

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Authors : Lazebnik, Kirill (Author of the conference)
CIRM (Publisher )

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Abstract : 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.

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
37F35 - Conformal densities and Hausdorff dimension

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 02/11/2021
    Conference Date : 21/09/2021
    Subseries : Research talks
    arXiv category : Complex Variables ; Dynamical Systems
    Mathematical Area(s) : Analysis and its Applications ; Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Video Time : 00:35:40
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-09-21_Lazebnik.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.19813003
Cite this video as: Lazebnik, Kirill (2021). Transcendental Julia sets of minimal Hausdorff dimension. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19813003
URI : http://dx.doi.org/10.24350/CIRM.V.19813003

See Also

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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