Skip to main content
Log in

Kovalevskaya numbers of generalized toda chains

  • 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

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

Instant access to the full article PDF.

Literature cited

  1. S. V. Kovalevskaya, Scientific Papers [in Russian], Izd. Akad. Nauk SSSR, Moscow (1948).

    Google Scholar 

  2. T. Bountis, H. Segur, and F. Vivaldi, “Integrable Hamiltonian systems and the Painlevé property,” Phys. Rev. A, General Physics,25, No. 3, 1257–1264 (1982).

    Google Scholar 

  3. Y. F. Chang, J. M. Greene, M. Tabor, and J. Weiss, “The analytic structure of dynamic systems and self-similar natural boundaries,” Physica D,8, No. 1, 183–207 (1983).

    Google Scholar 

  4. M. Adler and P. van Moerbeke, “Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization,” Commun. Math. Phys,83, No. 1, 83–106 (1982).

    Google Scholar 

  5. M. Ablowitz and H. Segar, Solitons and the Inverse Scattering Method [Russian translation], Mir, Moscow (1987).

    Google Scholar 

  6. M. Toda, Theory of Nonlinear Lattices [Russian translation], Mir, Moscow (1984).

    Google Scholar 

  7. O. I. Bogoyavlenskii, Methods of Qualitative Theory of Dynamic Systems in Astrodynamics and Gas Dynamics [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  8. O. I. Bogoyavlenski, “On pertrubations of the periodic Toda lattices,” Commun. Math. Phys.,56, 201–209 (1976).

    Google Scholar 

  9. S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York (1978).

    Google Scholar 

  10. E. K. Sklyanin, “Boundary conditions for integrable quantum systems,” LOMI Preprint, Leningrad (1986).

  11. V. V. Kozlov and D. V. Treshchev, “Polynomial integrals of Hamiltonian systems with expontial interaction,” Izv. AN SSSR, Ser. Mat.,53, No. 3, 537–556 (1989).

    Google Scholar 

  12. V. V. Kozlov, “Towards a perturbation theory for Hamiltonian systems with noncompact invariant surfaces,” Vest. Mosk. Gos. Univ., Ser. 1, Mat. Mekh., No. 2, 55–61 (1988).

    Google Scholar 

  13. A. M. Liapunov, “On a property of differential equations of motion of a heavy solid body with a fixed point,” in: Collected Works [in Russian], Vol. 1, Izd. AN SSSR, Moscow (1954), pp. 402–417.

    Google Scholar 

  14. H. Yoshida, “Necessary conditions for the existence of algebraic first integrals, I, II,” Cel.-Mech.,31, No. 4, 363–379, 381–399 (1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 46, No. 5, pp. 17–28, November, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kozlov, V.V., Treshchev, D.V. Kovalevskaya numbers of generalized toda chains. Mathematical Notes of the Academy of Sciences of the USSR 46, 840–848 (1989). https://doi.org/10.1007/BF01139615

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01139615

Keywords

Navigation