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The first focus quantity of a complex monodromic singular point

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Abstract

We consider the problem of distinguishing the center and focus in the case of a “strongly degenerate” singular point. A sufficient condition is explicitly stated for the existence of a focus for singular points of vector fields on the plane belonging to a certain class.

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Literature cited

  1. V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhizdat, Moscow-Leningrad (1947).

    Google Scholar 

  2. A. M. Lyapunov, General Problem of the Stability of Motion [in Russian], Gostekhizdat, Moscow-Leningrad (1950).

    Google Scholar 

  3. A. D. Bryuno, A Local Method of Nonlinear Analysis for Differential Equations [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  4. I. Bendixon, “Sur les courbes definies par des equations differentielles,” Acta Math.,24, 1–88 (1901).

    Google Scholar 

  5. F. Dumortier, “Singularities of vector fields on the plane,” J. Dif. Eq.,23, 53–106 (1977).

    Google Scholar 

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

    Google Scholar 

  7. Yu. S. Il'yashenko, “Singular points and limit cycles of differential equations on the real and complex plane,” Preprint ONTI NTsBI Academy of Sciences of the USSR, Pushchino (1982).

  8. V. I. Arnol'd, Supplementary Chapters to the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  9. H. Dulac, Limit Cycles [Russian translation], Nauka, Moscow (1980).

    Google Scholar 

  10. V. P. Nozdracheva, “A congruence function in a neighborhood of a structurally stable saddle,” Diff. Urav.,15, No. 2, 252–261 (1979).

    Google Scholar 

  11. R. I. Bogdanov, “Local orbital normal forms of vector fields on the plane,” Trudy sem. im. U. G. Petrovskogo, No. 5, 51–84 (1979).

    Google Scholar 

  12. K. T. Chen, “Equivalence and decomposition of vector fields about an elementary critical point,” Am. J. Math.,85, 693–722 (1963).

    Google Scholar 

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Authors
  1. N. B. Medvedeva
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Additional information

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 13, pp. 106–122, 1988.

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Medvedeva, N.B. The first focus quantity of a complex monodromic singular point. J Math Sci 50, 1421–1436 (1990). https://doi.org/10.1007/BF01097031

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  • DOI: https://doi.org/10.1007/BF01097031

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