Limit cycles for rigid cubic systems (Q1770980)

The authors consider three families of planar cubic systems with 0, 1 and 2 pairs of critical points at infinity, respectively. Simultaneously all of these systems have a unique finite singular point of center-focus type and constant angular velocity. The bifurcation diagrams for such families are presented. Also, the authors obtain the uniqueness of a limit cycle for two of these families and a lower bound for the number of limit cycles for the third family.