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Cauchy indices and the index of a singular point of a vector field

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Global Analysis — Studies and Applications II

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References

  1. Arnol’d V.I. The index of a singular point of a vector field, Petrovskiǐ-Oleinik inequalities, and Hodge mixed structures, Funkts. analiz i ego prilozheniya, 1978, v. 12, No.1 (in Russian).

    Google Scholar 

  2. Berezovskaya F.S. The index of a stationary point of a vector field on a plane, Funkts. analiz i ego prilozheniya, 1979, v. 13, No.2 (in Russian).

    Google Scholar 

  3. Bliznyakov N.M. and Mukhamadiev È.M. On the calculation of the index of a singular point of a polylinear vector field, Proc. Math. Department of Voronezh State University, 1971, No.4 (in Russian).

    Google Scholar 

  4. Bliznyakov N.M. Algebraic calculation of the index, in: Methods of solving operator equations, Voronezh, 1978 (in Russian).

    Google Scholar 

  5. Bliznyakov N.M. Calculation and estimates for a singular point of a vector field on a plane, Deposited at VINITI, August 14, 1979, No. 3041–79 (in Russian).

    Google Scholar 

  6. Gantmakher F.R. Theory of matrices. Moscow, 1967 (in Russian).

    Google Scholar 

  7. Zabreǐko P.P. and Krasnosel’skiǐ M.A. On the calculation of the index of an isolated fixed point of completely continuous vector field, Dokl. Akad. Nauk SSSR, 1961, v. 141, No.2 (in Russian).

    Google Scholar 

  8. Zabreǐko P.P. On the calculation of the Poincaré index, Dokl. Akad. Nauk SSSR, 1962, v. 145, No.5 (in Russian).

    Google Scholar 

  9. Zakalyukin V.M. Algebraic calculability of the index of a singular point of a vector field, Funkts. analiz i ego prilozheniya, 1972, v. 6, No.1 (in Russian).

    Google Scholar 

  10. Krasnosel’skiǐ M.A. and Zabreǐko P.P. Geometric methods in nonlinear analysis, Moscow, 1975 (in Russian).

    Google Scholar 

  11. Krasnosel’skiǐ M.A., Perov A.I., Povolotskiǐ A.I., and Zabreǐko P.P. Vector fields on a plane, Moscow, 1963 (in Russian).

    Google Scholar 

  12. Mukhamadiev È. On the calculation of rotation of a finite-dimensional vector field, Dokl. Akad. Nauk Tadjik SSR, 1967, v. 11, No.3 (in Russian).

    Google Scholar 

  13. Senchakova N.V. On the calculation of the Poincaré index of zero singular point of vector fields with homogeneous components, Vestnik Yaroslavskogo Universiteta, Yaroslavl’, 1975, No.12 (in Russian).

    Google Scholar 

  14. Khimshiashvili G.N. On local degree of smooth mapping, Soobshch. Akad. Nauk. Gruz. SSR, 1977, v. 85, No.2 (in Russian).

    Google Scholar 

  15. Khovanskiǐ A.G. Index of a polynomial vector field, Funkts. analiz i ego prilozheniya, 1979, v. 13, No.1 (in Russian).

    Google Scholar 

  16. Cherevichnyǐ P.T. Index of a singular point of the differential equation y′=P4(x,y) / Q4(x,y), Diff. uravneniya, 1977, v. 13, No.3 (in Russian).

    Google Scholar 

  17. Eisenbud D. and Levine H. An algebraic formula for the degree of a C map germ, Ann. Math., 1977, v. 106, No. 1.

    Google Scholar 

  18. Kronecker L. Über Systeme von Funktionen mehrerer Variabeln, Monatsberichte Berl. Acad., 1869.

    Google Scholar 

  19. Seidenberg A.A. A new decision method for elementary algebra, Ann. Math., 1954, ser. 2, v. 60.

    Google Scholar 

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Yuriǐ G. Borisovich Yuriǐ E. Gliklikh A. M. Vershik

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© 1986 Springer-Verlag

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Bliznyakov, N.M. (1986). Cauchy indices and the index of a singular point of a vector field. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis — Studies and Applications II. Lecture Notes in Mathematics, vol 1214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075956

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  • DOI: https://doi.org/10.1007/BFb0075956

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