Classification of 2-dimensional contracting rigid germs and Kato surfaces:I

A holomorphic germ f: (C-n, 0) is rigid if the increasing union of the crit ical set of all its iterate is a divisor with normal crossings. The aim of this article is to classify completely contracting rigid germs of (C-2, 0). There are seven different main classes of them. For each of them, we give simple (polynomial) normal forms, and we study their main features, their u nicity and their group of automorphisms. We give an application to the stud y of the geometry of the basin of attraction of the superattracting point o f a Henon mapping: this reproves old results of Hubbard and Obersta-Vorth a nd precise them. (C) 2000 Editions scientifiques et medicales Elsevier SAS.