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On new resonances and normal forms of autonomous systems with one zero eigenvalue

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Abstract

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has one zero eigenvalue, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to polynomial normal form.

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References

  1. V. S. Samovol, “Normal form of autonomous systems with one zero eigenvalue,” Mat. Zametki 75(5), 711–720 (2004) [Math. Notes 75 (5–6), 660–668 (2004)].

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  3. V. S. Samovol, “Equivalence of systems of differential equations in a neighborhood of a singular point,” in Trudy Moskov.Mat. Obshch. (Izd.Moskov. Univ., Moscow, 1982), Vol. 44, pp. 213–234 [in Russian].

    Google Scholar 

  4. A. N. Kuznetsov, “Differentiable solutions to degenerate systems of ordinary equations,” Funktsional. Anal. i Prilozhen. 6(2), 41–51 (1972) [Functional Anal. Appl. 6, 119–127 (1972)].

    Article  Google Scholar 

  5. G. R. Belitskii, “Smooth equivalence of germs of vector fields with a single zero eigenvalue or a pair of purely imaginary eigenvalues,” Funktsional. Anal. i Prilozhen. 20(4), 1–8 (1986) [Functional Anal. Appl. 20, 253–259 (1986)].

    MathSciNet  Google Scholar 

  6. Ph. Hartman, Ordinary Differential Equations (Wiley, New York, 1964; Mir, Moscow, 1970).

    MATH  Google Scholar 

  7. Yu. N. Bibikov, “Reducibility of a system of two differential equations to normal form,” Differ. Uravn. 7(10), 1899–1902 (1971) [in Russian].

    MATH  MathSciNet  Google Scholar 

  8. W. Wasow, Asymptotic Expansions for Ordinary Differential Equations (Wiley, New York-London-Sydney, 1965; Mir, Moscow, 1968).

    MATH  Google Scholar 

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Authors and Affiliations

  1. State University — Higher School of Economics, Moscow, Russia

    V. S. Samovol

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  1. V. S. Samovol
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Correspondence to V. S. Samovol.

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Original Russian Text © V. S. Samovol, 2010, published in Matematicheskie Zametki, 2010, Vol. 88, No. 1, pp. 63–77.

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Samovol, V.S. On new resonances and normal forms of autonomous systems with one zero eigenvalue. Math Notes 88, 67–78 (2010). https://doi.org/10.1134/S0001434610070072

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  • DOI: https://doi.org/10.1134/S0001434610070072

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