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Separatrices at singular points of planar vector fields

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Acta Mathematica

An Erratum to this article was published on 01 December 1983

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References

  1. Andronov, A. A., et al.,Qualitative Theory of Second Order Dynamic Systems. John Wiley and Sons, New York, 1973.

    MATH  Google Scholar 

  2. Bendixson, I., Sur les courbes définies par des équations différentielles.Acta Math., 24 (1901), 1–88.

    Article  MathSciNet  Google Scholar 

  3. Dumortier, F., Singularities of vector fields on the plane.J. Differential Equations, 23 (1977), 53–106.

    Article  MathSciNet  MATH  Google Scholar 

  4. Hartman, P.,Ordinary Differential Equations. John Wiley and Sons, New York, 1964.

    MATH  Google Scholar 

  5. Lefschetz, S., On a theorem of Bendixson.J. Differential Equations, 4 (1968), 66–101.

    Article  MathSciNet  MATH  Google Scholar 

  6. Schecter, S. &Singer, M. F., Planar Polynomial Foliations.Proc. Amer. Math. Soc., 79 (1980), 649–656.

    Article  MathSciNet  MATH  Google Scholar 

  7. Schecter, S. & Singer, M. F., Elliptic Sectors at Singular Points of Planar Vector Fields, unpublished.

  8. Seidenberg, A., Reduction of singularities of the differential equationAdy=Bdx.Amer. J. Math., 40 (1968), 248–269.

    Article  MathSciNet  Google Scholar 

  9. Takens, F., Singularities of vector fields.Publ. Math. I.H.E.S., 43 (1974), 47–100.

    MathSciNet  Google Scholar 

Added March 1980

  1. Berlinskii, A. N., On the number of elliptic domains adherent to a singularity.Soviet Math. Dokl., 9 (1968), 169–173.

    Google Scholar 

  2. —, On the structure of the neighborhood of a singular point of a two-dimensional autonomous system.Soviet Math. Dokl., 10 (1969), 882–885.

    MATH  Google Scholar 

  3. Sagalovich, M. E., Topological structure of the neighborhood of a critical point of a differential equation.Differential Equations, 11 (1975), 1498–1503.

    Google Scholar 

  4. —, Classes of local topological structures of an equilibrium state.Differential Equations, 15 (1979), 253–255.

    MATH  Google Scholar 

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An erratum to this article is available at http://dx.doi.org/10.1007/BF02393210.

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Schecter, S., Singer, M.F. Separatrices at singular points of planar vector fields. Acta Math. 145, 47–78 (1980). https://doi.org/10.1007/BF02414185

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  • DOI: https://doi.org/10.1007/BF02414185

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