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arXiv · 2208.00668

Topological entropy of a rational map over a complete metrized field

Charles Favre·Tuyen Trung Truong·Junyi Xie
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Abstract

We prove that the topological entropy of any dominant rational self-map of a projective variety defined over a complete non-Archimedean field is bounded from above by the maximum of its dynamical degrees, thereby extending a theorem of Gromov and Dinh-Sibony from the complex to the non-Archimedean setting. We proceed by proving that any regular self-map which admits a regular extension to a projective model defined over the valuation ring has necessarily zero entropy. To this end we introduce the e-reduction of a Berkovich analytic space, a notion of independent interest.

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Charles Favre, Tuyen Trung Truong, Junyi Xie. 2022-08-01. Topological entropy of a rational map over a complete metrized field. https://arxiv.org/abs/2208.00668

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