Classification of 2-dimensional contracting rigid germs and Kato surfaces. I
This paper is devoted to the analytic (and formal) classification of very special types of contracting germs in \((\mathbb{C}^2,0)\) and its application to the classification and the geometrical study of some compact analytic surfaces (Kato surfaces). The author classifies completely contracting rigid germs of \((\mathbb{C}^2,0)\) up to analytic and formal conjugacy and shows that these germs can be split into seven different classes. He shows that they are equivalent to very simple normal forms which are polynomial and their ``moduli'' spaces are finite-dimensional. Moreover, the authors gives an application to the study of the attraction of the superattracting point of a Hénon mapping [cf. \textit{J. H. Hubbard} and \textit{R. W. Oberste-Vorth}, Publ. Math. Inst. Hautes Étud. Sci. 79, 5-46 (1994; Zbl 0839.54029)].
scientific article; zbMATH DE number 1522072