Holomorphic motions of weighted periodic points

2023/07/24 by Bianchi, Fabrizio, Brévard, Maxence
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.12734

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.

Related

• Holomorphic motion for Julia sets of holomorphic families of endomorphisms of CP(k)
• Exponential equidistribution of periodic points for endomorphisms of \mathbb P^k
• Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)
• Propagation of equilibrium states in stable families of endomorphisms of \mathbb P^k(\mathbb C)
• Bifurcation currents in holomorphic dynamics on \bf P^k