English
Degeneration of rational maps and hyperbolic components - Lecture 1
Multi angle
Auteurs : Luo, Yusheng (Auteur de la Conférence)
CIRM (Editeur )
37F05 - Relations and correspondences
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F25 - Renormalisation
37P05 - Polynomial and rational maps
37P50 - Dynamical systems on Berkovich spaces
37F31 - Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics
CIRM (Editeur )
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Résumé :
In this mini course, I will discuss how degenerating sequences of rational maps can be studied using geometric and arithmetic tools. I will also discuss applications to study the boundary of hyperbolic components, length spectrum and rescaling limits, and some differences for sequences vs holomorphic families.
Keywords : complex dynamics; Berkovich space; R-trees; hyperbolic component
Codes MSC : Keywords : complex dynamics; Berkovich space; R-trees; hyperbolic component
37F05 - Relations and correspondences
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F25 - Renormalisation
37P05 - Polynomial and rational maps
37P50 - Dynamical systems on Berkovich spaces
37F31 - Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 10/02/2025 Date de captation : 20/01/2025 Sous collection : Research School arXiv category : Dynamical Systems ; Geometric Topology Domaine : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 00:59:27 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-01-20_Luo.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Etats de la recherche: Arithmetic, Algebraic and Analytics Dynamics / Etats de la recherche: Dynamique arithmétique, algébrique, et analytiqueOrganisateurs de la rencontre : Favre, Charles ; Gauthier, Thomas ; Raissy, Jasmin Dates : 20/01/2025 - 24/01/2025 Année de la rencontre : 2025 URL Congrès : https://conferences.cirm-math.fr/3211.html
Données de citation
DOI : 10.24350/CIRM.V.20290403Citer cette vidéo: Luo, Yusheng (2025). Degeneration of rational maps and hyperbolic components - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20290403 URI : http://dx.doi.org/10.24350/CIRM.V.20290403 |
Voir aussi
- [Virtualconference] Complexity theory in arithmetic dynamical systems - Lecture 3 / Auteur de la Conférence Xie, Junyi.
- [Virtualconference] Complexity theory in arithmetic dynamical systems - Lecture 2 / Auteur de la Conférence Xie, Junyi.
- [Multi angle] Degeneration of rational maps and hyperbolic components Lecture 3 / Auteur de la Conférence Luo, Yusheng.
- [Multi angle] Degeneration of rational maps and hyperbolic components - Lecture 2 / Auteur de la Conférence Luo, Yusheng.
- [Multi angle] The group of tame automorphisms - Lecture 3 / Auteur de la Conférence Lamy, Stéphane.
- [Multi angle] the group of tame automorphisms - Lecture 2 / Auteur de la Conférence Lamy, Stéphane.
- [Multi angle] Geometry and algebra of preperiodic points in $ \mathbb{P}^{N}$ - Lecture 3 / Auteur de la Conférence Demarco, Laura.
- [Multi angle] Geometry and algebra of preperiodic points in $ \mathbb{P}^{N}$ - Lecture 2 / Auteur de la Conférence Demarco, Laura.
- [Virtualconference] Complexity theory in arithmetic dynamical systems - Lecture 1 / Auteur de la Conférence Xie, Junyi.
- [Multi angle] the group of tame automorphisms - Lecture 1 / Auteur de la Conférence Lamy, Stéphane.
- [Multi angle] Geometry and algebra of preperiodic points in $ \mathbb{P}^{N}$ - Lecture 1 / Auteur de la Conférence Demarco, Laura.
- [Multi angle] Intersection theory and heights : birational perspective / Auteur de la Conférence Chambert-Loir, Antoine.
- [Multi angle] Rigidity and examples / Auteur de la Conférence Cantat, Serge.
Bibliographie
- LUO, Yusheng. Limits of rational maps, R-trees and barycentric extension. Advances in Mathematics, 2021, vol. 393, p. 108075. - https://doi.org/10.1016/j.aim.2021.108075
- LUO, Yusheng. Trees, length spectra for rational maps via barycentric extensions, and Berkovich spaces. Duke Mathematical Journal, 2022, vol. 171, no 14, p. 2943-3001. - https://doi.org/10.1215/00127094-2022-0056
- LUO, Yusheng. On hyperbolic rational maps with finitely connected Fatou sets. Journal of the London Mathematical Society, 2022, vol. 105, no 1, p. 500-542. - https://doi.org/10.1112/jlms.12525
- LUO, Yusheng. On geometrically finite degenerations I: boundaries of main hyperbolic components. Journal of the European Mathematical Society, 2023, vol. 26, no 10, p. 3793-3861. - https://doi.org/10.4171/jems/1342
- LUO, Yusheng. On geometrically finite degenerations II: convergence and divergence. Transactions of the American Mathematical Society, 2022, vol. 375, no 5, p. 3469-3527. - https://doi.org/10.1090/tran/8597
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