a1 Department of Mathematics, Zhejiang University, Hangzhou Zhejiang, Peoples Republic of China
In this paper we study the number and the relative position of the limit cycles of a plane quadratic system with a weak focus. In particular, we prove the limit cycles of such a system can never have (2, 2)-distribution, and that there is at most one limit cycle not surrounding this weak focus under any one of the following conditions:
(i) the system has at least 2 saddles in the finite plane,
(ii) the system has more than 2 finite singular points and more than 1 singular point at infinity,
(iii) the system has exactly 2 finite singular points, more than 1 singular point at infinity, and the weak focus is itself surrounded by at least one limit cycle.
(Received December 21 1990)