Non-Archimedean Techniques and Dynamical Degenerations

Abstract

We develop non-Archimedean techniques to analyze the degeneration of a sequence of rational maps of the complex projective line. We provide an alternative to Luo’s method which was based on ultra-limits of the hyperbolic 3-space. We build hybrid spaces using Berkovich theory which enable us to prove the convergence of equilibrium measures, and to determine the asymptotics of Lyapunov exponents.

Keywords

Degeneration of rational maps / Non-standard analysis / Minimal resultant

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Funding

China Sponsorship Council(SC-202108070159)

RIGHTS & PERMISSIONS

Peking University