Skip to main content
SpringerLink
Log in

Topological classification of integrable geodesic flows on orientable two-dimensional Riemannian manifolds with additional integral depending on momenta linearly or quadratically

  • Published:
Functional Analysis and Its Applications Aims and scope

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

References

  1. A. T. Fomenko, Symplectic Geometry. Methods and Applications [in Russian], Moscow State University (1988).

  2. A. T. Fomenko, “The topology of isoenergetic surfaces of integrable Hamiltonian systems and obstacles to integrability,” Izv. Akad. Nauk SSSR, Ser. Mat.,50, No. 6, 1276–1307 (1986).

    Google Scholar 

  3. A. T. Fomenko and H. Tsishang, “On typical topological properties of integrable Hamiltonian systems,” Izv. Akad. Nauk SSSR, Ser. Mat.,52, No. 2, 378–407 (1988).

    Google Scholar 

  4. A. V. Bolsinov, S. V. Matveev, and A. T. Fomenko, “Topological classification of integrable Hamiltonian systems with two degrees of freedom. The list of systems of low complexity,” Usp. Mat. Nauk,45, No. 2, 49–77 (1990).

    Google Scholar 

  5. G. D. Birkhoff, Dynamical Systems, Providence, Rhode Island (1966).

  6. V. N. Kolokol'tsov, “Geodesic flows on two-dimensional manifolds with an additional first integral polynomial in velocities,” Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 5, 994–1010 (1982).

    Google Scholar 

  7. V. N. Kolokol'tsov, “New examples of manifolds with closed geodesics,” Vestn. Mosk. Univ., Ser. 1, Mat. Mekh., No. 4, 80–82 (1984).

    Google Scholar 

  8. Nguen T'en Zung and A. T. Fomenko, “Topological classification of nondegenerate integrable Bott Hamiltonians on an isoenergetic three-dimensional sphere,” Usp. Mat. Nauk,45, No. 6, 91–111 (1990).

    Google Scholar 

  9. V. V. Kozlov, “Topological obstacles to integrability of natural mechanical systems,” Dokl. Akad. Nauk SSSR,249, No. 6, 1299–1302 (1979).

    Google Scholar 

  10. G. Darboux, Leçons sur la théorie generale des surfaces et les applications géometriques du calcul infinitesimal. Vol. 3. Paris, Gauthier—Villars (1891).

    Google Scholar 

  11. T. Levi-Civita, “Sulle transformazioni della equazioni dinamiche,” Annali Mat.,2, No. 24 (1896).

Download references

Authors
  1. Nguen T'en Zung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. S. Polyakova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. N. Selivanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 27, No. 3, pp. 42–56, July–September, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zung, N.T., Polyakova, L.S. & Selivanova, E.N. Topological classification of integrable geodesic flows on orientable two-dimensional Riemannian manifolds with additional integral depending on momenta linearly or quadratically. Funct Anal Its Appl 27, 186–196 (1993). https://doi.org/10.1007/BF01087536

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01087536

Keywords

Search

Navigation