English
Transcendental dynamics and infinite-dimensional Thurston theory
Multi angle
Auteurs : ... (Auteur de la Conférence)
... (Editeur )
37F20 - Combinatorics and topology in relation with holomorphic dynamical systems
37F34 - Teichmüller theory; moduli spaces of holomorphic dynamical systems
... (Editeur )
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Résumé :
In complex dynamics it is usually important to understand the dynamical behavior of critical (or singular) orbits. For quadratic polynomials, this leads to the study of the Mandelbrot set and of its complement. In our talk we present a classification of some explicit families of the transcendental entire functions for which all singular values escape, i.e. functions belonging to the complement of the 'transcendental analogue' of the Mandelbrot set. This classification allows us to introduce higher dimensional analogues of parameter rays and to explore their properties. A key ingredient is a generalization of the famous Thurston's Topological Characterization of Rational Functions, but for the case of infinite rather than finite postsingular set. Analogously to Thurston's theorem, we consider the sigma-iteration on the Teichmüller space and investigate its convergence. Unlike the classical case, the underlying Teichmüller space is infinite-dimensional which leads to a completely different theory.
Keywords : Thurston; Teichmüller space; transcendental entire function; iteration; complex dynamics
Codes MSC : Keywords : Thurston; Teichmüller space; transcendental entire function; iteration; complex dynamics
37F20 - Combinatorics and topology in relation with holomorphic dynamical systems
37F34 - Teichmüller theory; moduli spaces of holomorphic dynamical systems
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Informations sur la Vidéo
Langue : AnglaisDate de publication : 02/11/2021 Date de captation : 23/09/2021 Sous collection : Research talks arXiv category : Dynamical Systems Domaine : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 00:33:58 Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-23_Bogdanov.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexeDates : 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.19810803Citer cette vidéo: (2021). Transcendental dynamics and infinite-dimensional Thurston theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19810803 URI : http://dx.doi.org/10.24350/CIRM.V.19810803 |
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Bibliographie
- 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 IV: dependence on parameters and escape on (pre-) periodic rays. arXiv preprint arXiv:2104.13102, 2021. - https://arxiv.org/abs/2104.13102
