CIRM - Videos & books Library - Transcendental Thurston Theory for entire functions and compositions

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Résumé : 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

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

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https://videos.cirm-math.fr/2021-09-23_Shemyacov.mp4

Informations sur la Rencontre

Nom de la rencontre : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe
Dates : 20/09/2021 - 24/09/2021
Année de la rencontre : 2021
URL Congrès : https://conferences.cirm-math.fr/2546.html

Données de citation

DOI : 10.24350/CIRM.V.19815403
Citer cette vidéo: (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

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Bibliographie

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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