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Transcendental Thurston Theory for entire functions and compositions

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Authors : Shemyakov, Sergey (Author of the conference)
CIRM (Publisher )

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Abstract : Thurston's topological characterization theory asks whether there is a holomorphic dynamical system that realizes topological (even combinatorial) data, this often allows to describe all possible dynamical systems in a certain parameter space. I work on extending Thurston topological characterization theory to different classes of transcendental functions. In my talk I will start with some explicit families of functions for which we have established an extension of Thurston's theory, and then describe further extensions by compositions of such functions. The presented ideas are part of my PhD thesis under the supervision of Dierk Schleicher. This is work in progress.

Keywords : transcendental dynamical systems; Thurston theory; quadratic differentials; Teichmüller space

MSC Codes :
37E30 - Homeomorphisms and diffeomorphisms of planes and surfaces
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F45
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 02/11/2021
    Conference Date : 23/09/2021
    Subseries : Research talks
    arXiv category : Dynamical Systems
    Mathematical Area(s) : Dynamical Systems & ODE ; Geometry
    Format : MP4 (.mp4) - HD
    Video Time : 00:32:19
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-09-23_Shemyacov.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.19815403
Cite this video as: Shemyakov, Sergey (2021). Transcendental Thurston Theory for entire functions and compositions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19815403
URI : http://dx.doi.org/10.24350/CIRM.V.19815403

See Also

Bibliography

  • DOUADY, Adrien et HUBBARD, John H. A proof of Thurston's topological characterization of rational functions. Acta Mathematica, 1993, vol. 171, no 2, p. 263-297 - http://dx.doi.org/10.1007/BF02392534

  • HUBBARD, John, SCHLEICHER, Dierk, et SHISHIKURA, Mitsuhiro. Exponential Thurston maps and limits of quadratic differentials. Journal of the American Mathematical Society, 2009, vol. 22, no 1, p. 77-117. - http://dx.doi.org/10.1090/S0894-0347-08-00609-7

  • BOGDANOV, Konstantin. Infinite-dimensional Thurston theory and transcendental dynamics I: infinite-legged spiders. arXiv preprint arXiv:2102.00300, 2021. - https://arxiv.org/abs/2102.00300

  • BOGDANOV, Konstantin. Infinite-dimensional Thurston theory and transcendental dynamics II: classification of entire functions with escaping singular orbits. arXiv preprint arXiv:2102.10728, 2021. - https://arxiv.org/abs/2102.10728

  • BOGDANOV, Konstantin. Infinite-dimensional Thurston theory and transcendental dynamics III: entire functions with escaping singular orbits in the degenerate case. arXiv preprint arXiv:2104.12206, 2021. - https://arxiv.org/abs/2104.12206

  • BOGDANOV, Konstantin. Infinite-dimensional Thurston theory and transcendental dynamics IV: dependence on parameters and escape on (pre-) periodic rays. arXiv preprint arXiv:2104.13102, 2021. - https://arxiv.org/abs/2104.13102



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