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

Collection Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

Organizer(s) Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk
Date(s) 20/09/2021 - 24/09/2021
linked URL https://conferences.cirm-math.fr/2546.html
00:00:00 / 00:00:00
24 27

Transcendental Thurston Theory for entire functions and compositions

By Sergey Shemyakov

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.

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Citation data

  • DOI 10.24350/CIRM.V.19815403
  • Cite this video Shemyakov, Sergey (23/09/2021). Transcendental Thurston Theory for entire functions and compositions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19815403
  • URL https://dx.doi.org/10.24350/CIRM.V.19815403

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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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