Saddle-point-Saddle-focus singular cycles and existence of horseshoes

Abstract

In this paper we study a type of two singular point singular cycle where one heteroclinic orbit is the transversal intersection of the 2-dimensional stable manifold of one singular point and the 2-dimensional unstable manifold of other singular point. We show that this kind of singular cycle can give rise to a new mechanism of creation of chaos in 3-dimensional vector fields.