Distribution of Limit Cycles in Quadratic Systems with Finite Multiplicity Three

摘要

The report is the third in a series of reports on the classification of phaseportraits of quadratic systems with finite multiplicity M(f) = 3. As before, by a quadratic system is meant an autonomous system of ordinary differential equations x(dot) identically equal to P(x,y), and y(dot) identically equal to Q(x,y) and P(x,y), Q(x,y) are relatively prime real polynomials, which are not both linear. Chapter headings include the following: Quadratic systems with finite multiplicity 3 and a M(sub 1,1, sup i) type of critical point at infinity; Systems with possibly two nests of limit cycles; Systems with at most one nest of limit cycles; Weak critical points and limit cycles in quadratic systems with finite multiplicity M(f) = 3 and a M(sub 1,1, sup 0) type of infinite critical point; Bounded quadratic systems.