Jason Bell: A transcendental dynamical degree (NTWS 052)
Channel: Number Theory Web Seminar
Date: 2023-08-06

Abstract: The degree of a dominant rational map $f:\mathbb{P}^n\to \mathbb{P}^n$ is the common degree of its homogeneous components.  By considering iterates of $f$, one can form a sequence $\deg(f^n)$, which is submultiplicative and hence has the property that there is some $\lambda\ge 1$ such that $(\deg(f^n))^{1/n}\to \lambda$.  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 in which this dynamical degree is provably transcendental.  This is joint work with Jeffrey Diller and Mattias Jonsson.

Link to slides: https://drive.google.com/file/d/1IsyZBSJGHIjehgmggLw0ao3QjXUrG6M7

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Monday, November 16, 2020 (5pm PST, 8pm EST)
Tuesday, November 17, 2020 (1am GMT, 2am CET, 3am Israel Standard Time, 6:30am IST, 9am China Standard Time, 12pm AEDT, 2pm NZDT)