Geodesic
On embedding a Morse-Smale diffeomorphism on a~3-manifold in a~topological flow
Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1761-1784

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In this paper, for the case of 3-dimensional manifolds, we solve the Palis problem on finding necessary and sufficient conditions for a Morse-Smale cascade to embed in a topological flow. The set of such cascades is open in the space of all diffeomorphisms, while the set of arbitrary diffeomorphisms that embed in a smooth flow is nowhere dense. Also, we consider a class of diffeomorphisms that embed in a topological flow and prove that a complete topological invariant for this class is similar to the Andronova-Maier scheme and the Peixoto graph. Bibliography: 26 titles.
Keywords: Morse-Smale diffeomorphism, Morse-Smale cascade, embedding in a flow, dynamical systems on manifolds. 
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     author = {V. Z. Grines and E. Ya. Gurevich and V. S. Medvedev and O. V. Pochinka},
     title = {On embedding a {Morse-Smale} diffeomorphism on a~3-manifold in a~topological flow},
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     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_12_a4/}
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V. Z. Grines; E. Ya. Gurevich; V. S. Medvedev; O. V. Pochinka. On embedding a Morse-Smale diffeomorphism on a~3-manifold in a~topological flow. Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1761-1784. http://geodesic.mathdoc.fr/item/SM_2012_203_12_a4/