Does anyone know of papers that mention the classification of non-singular Morse-Smale (NMS) flows up to topological equivalency? I am particularly interested in the flows on manifolds of dimension 3. But all I can find so far is the paper by Bin Yu on the classification of the NMS flows defined on the three-sphere.



Topological classification of Morse-Smale flows
Generally, if you hope a very clean list (like topological classification of surfaces) to completely classify NMS flows on 3-manifolds (even in three sphere) up to topological equivalence. It seems hopeless. One reason is that heteroclinic trajectories
connecting saddle orbits will lead a complete list quite wild. 


If you reduce the requirement, there are several directions:


* if you only need to classify up to indexed links of periodic orbits, [Wada](http://projecteuclid.org/euclid.jmsj/1230128668) give a nice algorithm to deal with the question in three sphere;
* if you don't need a clean list, there exists an [attempt](http://arxiv.org/abs/math/0408231) to consider complete classification. But the list seems as complicated as NMS flows themselves;
* if we don't care "heteroclinic trajectories connecting saddle orbits" (Certainly this is very small subset of all NMS flows), we can do some discussions, for instance, see [here](http://arxiv.org/abs/1311.6568).


More intersting discussions of NMS flows on three manifolds always are connected with the other topics. The following directions are what I know:


* Similar the connection of gradient flows and handle decompositions, [Asimov](http://www.jstor.org/stable/1970972) connect NMS flows with round handle decompositions. And J. Morgan (1979) use it to nearly detect which 3-manifolds admitting NMS flows. And [Yano](http://link.springer.com/article/10.1007/BF01388724#) considered for a given 3-manifold, which homotopy classes of nonsingular vector fields admit MS flows.
* People use NMS flows to represent the homotopy classes of nonsingular vector fields, see [here](http://www.researchgate.net/publication/2106263_About_homotopy_classes_of_non-singular_vector_fields_on_the_three-sphere).
* there are intersting connection between the periodic orbits of some NMS flows and integrable Hamiltonian systems, see [here](http://www.worldscientific.com/doi/abs/10.1142/S0218216598000097).
* People use some parts of NMS flows to construct more complicated system, for instance, Anosov flows on 3-manifolds, see [here](http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2145184) and [here](http://msp.warwick.ac.uk/gt/2013/17-04/b043.xhtml).


