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- W4387322660 abstract "This is an expository article, originally written in Japanese, on a dynamical system over a non-archimedean field. The main viewpoint is from complex and non-archimedean potential theories. After quickly introducing the Berkovich projective line, the dynamical moduli space as a scheme, and the various height functions on the space of rational functions and on the dynamical moduli space, we first survey our study of Rumely's new equivariants in non-archimedean dynamics and then survey our complex geometric and arithmetic studies of the dynamical moduli space from our joint works with Thomas Gauthier and Gabriel Vigny. The latter include a precise version of McMullen's finiteness theorem on formally exact multiplier spectra and an effective solution of Silverman's conjecture on a comparison between the moduli height and the critical height (qualitatively, the Silverman-Ingram theorem). The final topic is a degeneration of complex dynamics." @default.
- W4387322660 created "2023-10-04" @default.
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- W4387322660 date "2023-10-02" @default.
- W4387322660 modified "2023-10-06" @default.
- W4387322660 title "A dynamical system over a non-archimedean field" @default.
- W4387322660 doi "https://doi.org/10.48550/arxiv.2310.01052" @default.
- W4387322660 hasPublicationYear "2023" @default.
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