Skip to main content
SpringerLink
Log in

Linearizability of Degenerate Singular Points of Binary Differential Equations

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

It is shown that a binary differential equation with typical linear part and degenerate singular point (0, 0) is linearizable at the point (0, 0) if and only if its monodromy group is commutative. The convergence of formal linearizing series is established in typical cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. W. Bruce and F. Tari, “On binary differential equations,” Nonlinearity, 8, No. 2, 255–271 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. A. Davydov, “Normal form of a differential equation, not solvable for the derivative, in a neighborhood of a singular point,” Funct. Anal. Appl. 19, 81–89 (1985).

    Article  MATH  Google Scholar 

  3. A. G. Kuz’min, “On the behavior of the characteristics of equations of mixed type near the line of degeneration,” Differ. Uravn. 17, 2052–3063 (1981).

  4. L. Dara, “Singularities generiques des équations différentielles multiformes” [in French], Bol. Soc. Bras. Mat. 6, 95–128 (1975).

    Article  MathSciNet  MATH  Google Scholar 

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

  6. C. Camacho, P. Sad, “Invariant varieties through singularities of holomorphic vector fields,” Ann. Math. 115, No. 3, 579–595 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  7. Yu. S. Il’yashenko and S. Yu. Yakovenko, Analytic Theory of Differential Equations. Vol. 1 [in Russian], MTsNMO, Moscow (2013).

  8. H. Grauert, “Über Modifikationen und exzeptionelle analytische Mengen,” Math. Ann., 146, 331–368 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  9. S. M. Voronin, “Orbital analytic equivalence of degenerate singular points of holomorphic vector fields on the complex plane,” Proc. Steklov Inst. Math. 213, 30–49 (1996).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chelyabinsk State University, 129, Brat’ev Kashiriny St, Chelyabinsk, 454021, Russia

    S. M. Voronin & E. A. Cherepanova

Authors
  1. S. M. Voronin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Cherepanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. M. Voronin.

Additional information

Translated from Problemy Matematicheskogo Analiza 121, 2023, pp. 17-34.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Voronin, S.M., Cherepanova, E.A. Linearizability of Degenerate Singular Points of Binary Differential Equations. J Math Sci 269, 143–164 (2023). https://doi.org/10.1007/s10958-023-06266-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-023-06266-8

Search

Navigation