Holomorphic motions of weighted periodic points

Fabrizio Bianchi (1, 2) , Maxence Brévard (3, 4)

1 CNRS - Centre National de la Recherche Scientifique
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 UT3 - Université Toulouse III - Paul Sabatier
4 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Equidistribution; Periodic points; Holomorphic motion; Equilibrium states

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Fabrizio Bianchi, Maxence Brévard. Holomorphic motions of weighted periodic points. 2023. ⟨hal-04168492⟩