Attracting domains for semi-attractive transformations of \(\mathbb{C}^ p\)
A germ \(F\) of analytic transformation of \((\mathbb{C}^p, 0)\) is called semi-attractive at the origin, if \(F_{(0)}'\) has one eigenvalue equal to 1 and if the other ones are of modulus strictly less than 1. The main result is: either there exists a curve of fixed points, or \(F-I\) has multiplicity \(k\) and there exists a domain of attraction with \(k - 1\) petals. The case where \(F\) is a global isomorphism of \(C^2\) and \(F - I\) has multiplicity \(k\) at the origin is also studied.
scientific article; zbMATH DE number 791196