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Transactions of the American Mathematical Society

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Denjoy-type flows on orientable $ 2$-manifolds of higher genus


Author: Carl S. Hartzman
Journal: Trans. Amer. Math. Soc. 186 (1973), 219-227
MSC: Primary 58F20; Secondary 34C40
DOI: https://doi.org/10.1090/S0002-9947-1973-0362405-5
MathSciNet review: 0362405
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Abstract: The author generalizes A. Denjoy's theory of flows on a torus to compact orientable 2-manifolds of higher genus. Natural extensions of A. Denjoy's hypotheses are made and necessary conditions that a flow satisfy the new hypotheses are given.


References [Enhancements On Off] (What's this?)

  • [1] A. Denjoy, Sur les courbes définies par les équations differentielles à la surface du tore, J. Math. Pures Appl. (9) 11 (1932), 333-375.
  • [2] P. Hartman, Ordinary differential equations, Wiley, New York, 1964. MR 30 #1270. MR 0171038 (30:1270)
  • [3] C. S. Hartzman, Transversals to the flow induced by a differential equation on compact orientable 2-dimensional manifolds, Trans. Amer. Math. Soc. 167 (1972), 359-368. MR 45 #3879. MR 0294811 (45:3879)
  • [4] J. Milnor, Topology from the differentiable viewpoint, University of Virginia Press, Charlottesville, Va., 1965. MR 37 #2239. MR 0226651 (37:2239)
  • [5] V. V. Nemyckiĭ and V. V. Stepanov, Qualitative theory of differential equations, OGIZ, Moscow, 1947; English transl., Princeton Math. Series, no. 22, Princeton, Univ. Press, Princeton, N. J., 1960. MR 22 #12258. MR 0029483 (10:612h)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0362405-5
Keywords: Flows, 2-manifolds
Article copyright: © Copyright 1973 American Mathematical Society

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