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arXiv · 1601.03910

Growth of the number of periodic points for meromorphic maps

Tien-Cuong Dinh·Viet-Anh Nguyen·Tuyen Trung Truong
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Abstract

We show that any dominant meromorphic self-map f of a compact Kaehler manifold X is an Artin-Mazur map. More precisely, if P_n(f) is the number of its isolated periodic points of period n (counted with multiplicity), then P_n(f) grows at most exponentially fast with respect to n and the exponential rate is at most equal to the algebraic entropy of f. Further estimates are given when X is a surface. Among the techniques introduced in this paper, the h-dimension of the density between two arbitrary positive closed currents on a compact Kaehler surface is obtained.

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Tien-Cuong Dinh, Viet-Anh Nguyen, Tuyen Trung Truong. 2016-01-15. Growth of the number of periodic points for meromorphic maps. https://doi.org/10.1112/blms.12082

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