SPHERICAL HYPERSURFACES AND LATTES RATIONAL MAPS

Any rational map f is induced on the Riemann sphere by a homogeneous n on-degenerate polynomial map F on C-2. By the work of J. E. Fornaess a nd N. Sibony or J. Hubbard and P. Papadopol, one knows that b Omega(F) , the boundary of the basin of attraction of F at the origin, is Levi- flat above the Fatou set of f. Nothing is known about b Omega(F) when the Fatou set of f is empty. In this direction, we characterize the La ttes rational maps by a geometrical property of b Omega(F). It turns o ut that these basins, which we explicitely describe, are the first exa mples of essentially strictly pseudoconvex domains which do admit non- injective proper holomorphic self-maps. (C) Elsevier, Paris.