THEORY OF VALUES OF SINGULAR POINT IN COMPLEX AUTONOMOUS DIFFERENTIAL SYSTEMS

Consider the complex autonomous differential system (E). The main results of this paper are as follows: (i) The concept of values of singular point has been defined. It can realize the unity between the saddle values and the focal values in real systems, (ii) By defining the concept of the Lie-invariant, the constructive theorem of values of singular point and the extended symmetric principle can be obtained. (iii) All the 120 elementary Lie-invariants of (E3) have been computed. The constructive theorem being used, formulas of values of singular point and the integrability conditions of (E2) and (E(3)3) have been derived.