On existence of noncompact heteroclinic curves (Q1431462)

This paper deals with the class of Morse-Smale diffeomorphisms of three-dimensional manifolds whose nonwandering set consists of exactly four points two of which are saddles. For three-manifolds for which the sphere \(S^3\) is the universal covering under the above assumptions, the authors prove that the wandering set of the diffeomorphism has at least one nonclosed heteroclinic curve.