Hakim, Monique Attracting domains for semi-attractive transformations of \(\mathbb{C}^ p\). (English) Zbl 0832.58031 Publ. Mat., Barc. 38, No. 2, 479-499 (1994). 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. Reviewer: V.G.Angelov (Sofia) Cited in 18 Documents MSC: 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 37C70 Attractors and repellers of smooth dynamical systems and their topological structure Keywords:semi-attractive transformations; domain of attraction PDFBibTeX XMLCite \textit{M. Hakim}, Publ. Mat., Barc. 38, No. 2, 479--499 (1994; Zbl 0832.58031) Full Text: DOI EuDML