Exponential equidistribution of periodic points for endomorphisms of \mathbb P^k

2024/09/29 by de Thélin, Henry, Dinh, Tien-Cuong, Kaufmann, Lucas
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.19787

Abstract

Let f be a holomorphic endomorphism of \mathbb P^k of algebraic degree d≥ 2. We show that the periodic points of f of period n equidistribute towards the equilibrium measure of f exponentially fast as n tends to infinity. This quantifies a theorem of Lyubich for k=1 and of Briend-Duval for k≥ 2. A byproduct of our proof is the existence of a large number of periodic cycles in the small Julia set with large multipliers.

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