Holomorphic motions of weighted periodic points

TL;DR

This paper investigates how repelling periodic points in complex dynamical systems move holomorphically within stable families, establishing their asymptotic distribution with respect to natural measures in the Julia sets.

Contribution

It introduces new results on the asymptotic equidistribution of graphs of periodic points in holomorphic motions within complex projective spaces.

Findings

Asymptotic equidistribution of periodic point graphs

Holomorphic motions of repelling periodic points

Distribution results in Julia sets

Abstract

We study the holomorphic motions of repelling periodic points in stable families of endomorphisms of $\mathbb P^k (\mathbb C)$. In particular, we establish an asymptotic equidistribution of the graphs associated to such periodic points with respect to natural measures in the space of all holomorphic motions of points in the Julia sets.