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Transcendental dynamical degrees of birational maps

Apparaît dans la collection : Galois differential Theories and transcendence Thematic Month Week 4 / Théories de Galois différentielles et transcendance Mois thématique semaine 4

The degree of a dominant rational map $f: \mathbb{P}^n \rightarrow \mathbb{P}^n$ is the common degree of its homogeneous components. By considering iterates of $f$, one can form a sequence $\operatorname{deg}\left(f^n\right)$, which is submultiplicative and hence has the property that there is some $\lambda \geq 1$ such that $\left(\operatorname{deg}\left(f^n\right)\right)^{1 / n} \rightarrow \lambda$. The quantity $\lambda$ is called the first dynamical degree of $f$. We'll give an overview of the significance of the dynamical degree in complex dynamics and describe an example of a birational self-map of $\mathbb{P}^3$ in which this dynamical degree is provably transcendental. This is joint work with Jeffrey Diller, Mattias Jonsson, and Holly Krieger.

Informations sur la vidéo

Date de captation 18/02/2025
Date de publication 07/03/2025
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20308003
Citer cette vidéo Bell, Jason (18/02/2025). Transcendental dynamical degrees of birational maps. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20308003
URL https://dx.doi.org/10.24350/CIRM.V.20308003

Domaine(s)

Bibliographie

BELL, Jason P., DILLER, Jeffrey, JONSSON, Mattias, et al. Birational maps with transcendental dynamical degree. Proceedings of the London Mathematical Society, 2024, vol. 128, no 1, p. e12573. - https://doi.org/10.1112/plms.12573

Codes MSC

32H50 Iteration problems

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