Exemples de Lattès et domaines faiblement sphériques de ℂ n

Abstract

We describe the attracting basins of the origin in ℂ k+1 for the polynomial lifts of Lattes examples. We show that the boundary of these bounded pseudoconvex domains is a quotient of a compact spherical hypersurface, and we describe the singularities that appear. These domains are surprising, because they are very close to the ball, and admit non injective proper holomorphic self-maps. We also explicit some Lattes examples in dimension 2.