AROUND THE POINCARE CENTER-FOCUS PROBLEM

Abstract

It is well known that many mathematical models use differential equation systems and apply the qualitative theory of differential equations, introduced by Poincar´e and Liapunoff. One of the problems that persists in order to control the behavior of systems of this type, is to distinguish between a focus or a center (the Center-Focus Problem). The solving of this problem goes through the computation of the Poincar´e Liapunoff quantities. The problem of estimating the maximal number of algebraically  independent essential constants is called the Generalized Center-Focus Problem. The present article contains: some moments related to the history of the Center-Focus Problem; the contribution of the Academician C. Sibirschi’s
school in the solving of the Center-Focus Problem; methodological aspects of the M. N. Popa and V. V.
Pricop solution of the Generalized Center-Focus Problem.