2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68764This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local stable sets in the non-hyperbolic case. The author hopes to keep the survey up to date, and thus it would be grateful to anybody pointing out missing (or mistaken) results and references, and/or suggesting topics to be included or expanded in it.Plain-TeX file, 22 pages, to be published in the proceedings of the 13th Seminar on analysis and its applications, Isfahan, March 16-17, 2003Dynamical SystemsComplex Variables37F99 (Primary); 37F50, 32H50 (Secondary)text