Lorenz like Smale flows on three-manifolds

In this paper, we discuss how to realize Lorenz like Smale flows (LLSF) on 3-manifolds. It is an extension of M. Sullivan's work about Lorenz Smale flows on S3. We focus on two questions: (1) Classify the topological conjugate classes of LLSF which can be realized on S3; (2) Which 3-manifolds admit LLSF? If some 3-manifold admits LLSF, how does it admit LLSF? This paper is in some sense parallel to the work of J. Morgan and M. Wada on Morse–Smale flows on 3-manifolds.