Commentarii Mathematici Helvetici

, Volume 39, Issue 1, pp 97–110 | Cite as

Common singularities of commuting vector fields on 2-manifolds

  • Elon L. Lima


Vector Field Isotropy Group Compact Manifold Genus Zero Simple Closed Curve 
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  1. [1]
    H. Levine,Homotopie curves on surfaces. Proc. Am. Math. Soc.14 (1963), pp. 986–990.zbMATHCrossRefGoogle Scholar
  2. [2]
    E. Coddington andN. Levinson,Theory of Ordinary Differential Equations. Mc-Graw-Hill, New York (1955).zbMATHGoogle Scholar
  3. [3]
    A. Denjoy,Sur les courbes définies par des équations differentielles à la surface du tore. J. Math. Pures Appl. (9) 11 (1932), pp. 333–345.zbMATHGoogle Scholar
  4. [4]
    E. Lima,Commuting vector fields on S 2. Proc. Am. Math. Soc.15 (1964), pp. 138–141.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    E. Lima,Commuting vector fields on 2-manifolds. Bull. Am. Math. Soc.69 (1963), pp. 366–368.zbMATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    M. Peixoto,Structural stability on two-dimensional manifolds. Topology1 (1962), pp. 101–120.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    A. Schwartz,A generalization of the Poincaré-Bendixon theorem for two-dimensional manifolds. (To appear in the Am. Journal Math.).Google Scholar
  8. [8]
    H. Whitney,Regular families of curves. Ann. of Math.34 (1933), pp. 244–270.CrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag 1965

Authors and Affiliations

  • Elon L. Lima
    • 1
    • 2
  1. 1.Columbia UniversityNew York
  2. 2.I. M. P. A.Rio de JaneiroBrazil

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