Geodesic
Classification of Morse--Smale flows on two-dimensional manifolds
Sbornik. Mathematics, Tome 189 (1998) no. 8, pp. 1205-1250

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The problem of topological trajectory classification of Morse–Smale flows on closed two-dimensional surfaces is considered. Important results in this direction have been obtained by Peixoto and his school. However, the complete solution of this problem has not yet been accurately presented. The new topological invariants constructed in our work have a simpler form than those in the works of Peixoto. In particular, a list of Morse–Smale flows of small complexity is given which has been obtained by the authors by means of the invariants constructed by them. 
@article{SM_1998_189_8_a5,
     author = {A. A. Oshemkov and V. V. Sharko},
     title = {Classification of {Morse--Smale} flows on two-dimensional manifolds},
     journal = {Sbornik. Mathematics},
     pages = {1205--1250},
     publisher = {mathdoc},
     volume = {189},
     number = {8},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_8_a5/}
}
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A. A. Oshemkov; V. V. Sharko. Classification of Morse--Smale flows on two-dimensional manifolds. Sbornik. Mathematics, Tome 189 (1998) no. 8, pp. 1205-1250. http://geodesic.mathdoc.fr/item/SM_1998_189_8_a5/