Jason Bell, Waterloo

Title: Transcendental dynamical degrees of birational maps.

Abstract: The degree of a dominant rational map $f:mathbb{P}^n o mathbb{P}^n$ is the common degree of its homogeneous components. By considering iterates of $f$, one can form a sequence ${ m deg}(f^n)$, which is submultiplicative and hence has the property that there is some $lambdage 1$ such that $({ m deg}(f^n))^{1/n} o lambda$. 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.

Québec-Vermont Number Theory Seminar
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