FUNCTIONAL INVARIANTS IN ONE PROBLEM OF LOCAL ANALYTICAL CLASSIFICATION

The investigation objects are the special points of the holomorphic vector fields on the complex plane. The aim is to construct the total system of invariants in the task about analytical classification of the saddle resonant special points on the complex plane. The formal classification of t-shifts has been obtained; the analytical classification of t-shifts in the resonant case has been obtained, it doesn't coincid with formal one and has the functional modules. The analytical classification of the saddle resonant special points of the holomorphic vector fields on the complex plane has been obtained. This classification doesn't coincide with formal one and has the functional modules; the simple sufficient conditions on the analytical equivalency of the saddle resonant vector field growth and its formal standard shape have been found. The results permitting to solve completely the about analytical classification of the saddle resonant special points on the complex plane and there by in the resonant case to complete the programme on the local investigation of the special points of holomorphic vector fields on the complex plane, proposed by A. Poincare have been obtainedAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio