Lower Bounds for Galois Orbits of periodic points for polarized endomorphisms

2025/12/02 by Jit Wu Yap, Yap, Jit Wu, Tien‐Cuong Dinh +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2512.02343

Abstract

Let K be a number field, X a smooth projective variety over K and f: X → X a polarized endomorphism of degree d ≥ 2. We prove an exponential lower bound on [K(\Per_n):K], where \Per_n is the set of n-periodic points, extending results of [Yap24] to higher dimensions. We also prove a quantitative rate of equidistribution for \Per_n to the equilibrium measure.

Citations

• Quantitative equidistribution of periodic points for rational maps
• Arakelov-Green's functions for dynamical systems on projective varieties
• Periodic points for meromorphic self-maps of Fujiki varieties
• Equidistribution speed for endomorphisms of projective spaces
• Equidistribution quantitative des points de petite hauteur sur la droite projective
• Questions on self maps of algebraic varieties

Related

• Quantitative Equidistribution of Small Points for Canonical Heights
• Equidistribution of periodic points of some automorphisms on K3 surfaces
• Uniform Bounds for Periods of Endomorphisms of Varieties
• Exponential equidistribution of periodic points for endomorphisms of \mathbb P^k
• A proof of the Andre-Oort conjecture for A_g