Advertisement

Functional Analysis and Its Applications

, Volume 32, Issue 3, pp 172–182 | Cite as

Maslov index and symplectic sturm theorems

  • P. E. Pushkar'
Article

Keywords

Singular Point Maslov Index Positive Vector Hamiltonian Vector Field Nonsingular Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. I. Arnold, “On the characteristic class entering into conditions of quantization,” Funkts. Anal. Prilozhen.,1, No. 1, 1–14 (1967).zbMATHCrossRefGoogle Scholar
  2. 2.
    V. I. Arnold, “The Sturm theorems and symplectic geometry,” Funkts. Anal. Prilozhen.,19, No. 4, 1–10 (1985).zbMATHGoogle Scholar
  3. 3.
    V. I. Arnold. Ordinary Differential Equations [in Russian], Nauka, Moscow, 1984.Google Scholar
  4. 4.
    R. Bott, “On the iterations of closed geodesics and the Sturm intersection theory,” Comm. Pure Appl. Math.,9, No. 2, 171–206 (1956).zbMATHMathSciNetGoogle Scholar
  5. 5.
    H. M. Edwards, “A generalized Sturm theorem,” Ann. Math.,80, No. 1, 22–57 (1964).zbMATHCrossRefGoogle Scholar
  6. 6.
    L. Gärding, “An inequality for hyperbolic polynomials,” J. Math. Mech.,8, No. 6, 957–965 (1959).MathSciNetGoogle Scholar
  7. 7.
    A. B. Givental, “Sturm's theorem for hyperelliptic integrals,” Algebra Analiz,1, No. 5, 95–102 (1989).MathSciNetGoogle Scholar
  8. 8.
    A. B. Givental, “Nonlinear generalization of the Maslov index,” Adv. Sov. Math., Vol.1, 1990, pp. 71–103.zbMATHMathSciNetGoogle Scholar
  9. 9.
    V. B. Lidskii, “Oscillation theorems for canonical system of differential equations,” Dokl. Akad. Nauk SSSR,105, No. 5, 877–880 (1955).MathSciNetGoogle Scholar
  10. 10.
    M. Morse, “A generalization of the Sturm theorems inn-space,” Math. Ann.,103, 52–69 (1930).zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    M. Morse, “The calculus of variation in the large,” In: AMS Coll. Publ., Vol. 18, New York, 1934, pp. 80–106.Google Scholar
  12. 12.
    J. Robbin and D. Salamon, “The Maslov index for paths,” Topology,32, No. 4, 827–844 (1993).zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    C. Sturm, “Memoire sur les equaitions differentielles du second ordre,” J. Math. Pures Appl.,1, 106–186 (1836).Google Scholar
  14. 14.
    A. G. Khovanskii, “Analogues of Aleksandrov-Fenchel inequalities for hyperbolic forms,” Dokl. Akad. Nauk SSSR,276, No. 6, 1332–1334 (1984).zbMATHMathSciNetGoogle Scholar
  15. 15.
    V. A. Yakubovich, “Arguments on the group of symplectic matrices,” Mat. Sb.,55, No. 3, 255–280 (1961).zbMATHMathSciNetGoogle Scholar
  16. 16.
    V. A. Yakubovich, “Oscillatory properties of solutions of canonical equations,” Mat. Sb.,56, No. 1, 3–42 (1962).zbMATHMathSciNetGoogle Scholar
  17. 17.
    V. A. Yakubovich, “Nonoscillation of linear periodic Hamiltonian equations and related problems,” Algebra Analiz,3, No. 5, 229–253 (1991).zbMATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • P. E. Pushkar'

There are no affiliations available

Personalised recommendations