Approximability of dynamical systems between trees of spheres

Matthieu Arfeux (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We study sequences of analytic conjugacy classes of rational maps which diverge in moduli space. In particular, we are interested in the notion of rescaling limits introduced by Jan Kiwi. In the continuity of [A1] we recall the notion of dynamical covers between trees of spheres for which a periodic sphere corresponds to a rescaling limit. We study necessary conditions for such a dynamical cover to be the limit of dynamically marked rational maps. With these conditions we classify them for the case of bicritical maps and we recover the second main result of Jan Kiwi regarding rescaling limits.

Mots clés: dynamique holomorphe; arbres de sphères; compactification; fractions rationnelles marquées

Domaines: Systèmes dynamiques [math.DS]

Matthieu Arfeux. Approximability of dynamical systems between trees of spheres. 2014. ⟨hal-01053432⟩