Degeneration of rational maps and hyperbolic components - Lecture 1 | Vidéo | Carmin.tv

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Degeneration of rational maps and hyperbolic components - Lecture 1

Apparaît dans la collection : Etats de la recherche: Arithmetic, Algebraic and Analytics Dynamics / Etats de la recherche: Dynamique arithmétique, algébrique, et analytique

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.

Informations sur la vidéo

Date de captation 20/01/2025
Date de publication 10/02/2025
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20290403
Citer cette vidéo Luo, Yusheng (20/01/2025). Degeneration of rational maps and hyperbolic components - Lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20290403
URL https://dx.doi.org/10.24350/CIRM.V.20290403

Domaine(s)

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

Codes MSC

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