Abstract
The paper contains the classification up to conjugation in the categoryC k,k=1,...,∞, of complete nondegenerate divergence-free vector fieldson a compact surface (possibly with boundary) almost all of whose trajectories are closed. The classification up to conjugation in given for arbitrary nondegenerate divergence-free vector fields on the surfacesS 2,\(\mathbb{R}P^2 \),K 2,T 2,\(K^2 \# \mathbb{R}P^2 \), possibly with holes.
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Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 336–353 March, 1999.
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Kruglikov, B.S. Exact classification of nondegenerate devergence-free vector fields on surfaces of small genus. Math Notes 65, 280–294 (1999). https://doi.org/10.1007/BF02675069
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DOI: https://doi.org/10.1007/BF02675069