Degeneration of rational maps and hyperbolic components Lecture 3 | Vidéo | Carmin.tv

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Degeneration of rational maps and hyperbolic components Lecture 3

Appears in 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.

Information about the video

Date of recording 21/01/2025
Date of publication 10/02/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20291103
Cite this video Luo, Yusheng (21/01/2025). Degeneration of rational maps and hyperbolic components Lecture 3. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20291103
URL https://dx.doi.org/10.24350/CIRM.V.20291103

Domain(s)

Bibliography

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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