Bifurcation of limit cycles from a separatrix contour in three-parameter families of dynamical systems on orientable two-dimensional manifolds (Q2703848)

Here, a family of dynamical systems with parameters on an orientable two-dimensional compact manifold is considered. The number and stability of limit cycles bifurcating from the considered singular trajectories and represented the corresponding phase portraits are completely described.NEWLINENEWLINENEWLINEIt is proved that the destruction of a contour consisting of separatrices of two saddles and a homoclinic loop results in the bifurcation of at most two limit cycles of opposite stability. In this case, each cycle divides the original manifold so that saddles do not have interesting neighborhoods disjoint with the cycles themselves.