Skip to main content
SpringerLink
Log in

Surfaces defined by hyperbolic equations

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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

Literature cited

  1. V. I. Arnol'd, “Contact structure, relaxational oscillations, and singular points of implicit differential equations,” in: Geometry and the Theory of Singularities in Nonlinear Equations [in Russian], Voronezh State Univ. (1987).

  2. A. A. Davydov, “Normal form of slow motions of equations of relaxational type and fibrations of binomial surfaces,” Mat. Sb.,132 (174), No. 1, 131–139 (1987).

    Google Scholar 

  3. V. I. Arnol'd, Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  4. V. I. Arnol'd, Supplementary Chapters of the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  5. V. P. Kostov, “Versal deformations of forms of degree M on the line,” Funkts. Anal. Prilozhen.,18, No. 4, 81–82 (1984).

    Google Scholar 

  6. B. Malgrange, Ideals of Differentiable Functions [Russian translation], Mir, Moscow (1968).

    Google Scholar 

  7. L. R. Volevich and V. Ta. Ivrii, “Hyperbolic equations,” in: I. G. Petrovskii, Selected Works. Systems of Partial Differential Equations. Algebraic Geometry [in Russian], Nauka, Moscow (1986), pp. 395–418.

    Google Scholar 

  8. V. I. Arnol'd, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Mappings [in Russian], Vol. I, Nauka, Moscow (1982).

    Google Scholar 

  9. J. Martinet, “Sur les singularitees des formes differentielles,” Ann. Inst. Fourier,20, No. 1, 95–178 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR, USSR

    V. I. Arnol'd

Authors
  1. V. I. Arnol'd
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 44, No. 1, pp. 3–18, July, 1988.

The author thanks D. G. Vasil'ev, Yu. S. ll'yashenko, and A. B. Givental' for helpful discussions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arnol'd, V.I. Surfaces defined by hyperbolic equations. Mathematical Notes of the Academy of Sciences of the USSR 44, 489–497 (1988). https://doi.org/10.1007/BF01158112

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158112

Keywords

Search

Navigation