This article is cited in 61 papers

Classification of Morse–Smale flows on two-dimensional manifolds

A. A. Oshemkov^a, V. V. Sharko<sup>b

a</sup> M. V. Lomonosov Moscow State University
^b Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: 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.

UDC: 513.83

MSC: 34C35, 58F09

Received: 13.11.1997

DOI: 10.4213/sm341

 English version: Sbornik: Mathematics, 1998, 189:8, 1205–1250

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