Local structure of analytic transformations of two complex variables. II (Q1191308)

This paper is a continuation of the author's previous work [part I of this paper, ibid. 26, No. 2, 233-261 (1986; Zbl 0611.32001)] regarding holomorphic mappings \(T:\mathbb{C}^ 2\to\mathbb{C}^ 2\) with \(T(0)=0\). \(T\) is said to be of type \((1,b)\) if the eigenvalues of its linear part are 1 and \(b\). Here the author establishes some intrinsic properties of certain particular cases of type \((1,b)_ 1\). For such a particular transformation \(T\), the author proves the following results: Theorem 1: There exists some injective holomorphic mapping \(H:\mathbb{C}\to M\) into some 2-dimensional \(\mathbb{C}\)-analytic manifold \(M\), such that the simple convergent points of \(T^{-1}=H(\mathbb{C})\cup\{0\}\). Theorem 2: The set of all uniformly convergent points of \(T\) has a non empty intersection with \(H(A)\), where \(A\) is some domain in \(\mathbb{C}\).