Equidistribution of periodic points of some automorphisms on K3 surfaces

2011/02/23 by Lee, Chong Gyu
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1102.4860

Abstract

We say (W, \ϕ₁,..., ϕ_t\) is a polarizable dynamical system of several morphisms if ϕ_i are endomorphisms on a projective variety W such that \bigotimes ϕ_i^*L is linearly equivalent to L^q for some ample line bundle L on W and for some q>t. If q is a rational number, then we have the equidistribution of small points of given dynamical system because of Yuan's work. As its application, we can build a polarizable dynamical system of an automorphism and its inverse on K3 surface and show its periodic points are equidistributed.

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