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Maslov index and symplectic sturm theorems

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References

  1. V. I. Arnold, “On the characteristic class entering into conditions of quantization,” Funkts. Anal. Prilozhen.,1, No. 1, 1–14 (1967).

    Article  MATH  Google Scholar 

  2. V. I. Arnold, “The Sturm theorems and symplectic geometry,” Funkts. Anal. Prilozhen.,19, No. 4, 1–10 (1985).

    MATH  Google Scholar 

  3. V. I. Arnold. Ordinary Differential Equations [in Russian], Nauka, Moscow, 1984.

    Google Scholar 

  4. R. Bott, “On the iterations of closed geodesics and the Sturm intersection theory,” Comm. Pure Appl. Math.,9, No. 2, 171–206 (1956).

    MATH  MathSciNet  Google Scholar 

  5. H. M. Edwards, “A generalized Sturm theorem,” Ann. Math.,80, No. 1, 22–57 (1964).

    Article  MATH  Google Scholar 

  6. L. Gärding, “An inequality for hyperbolic polynomials,” J. Math. Mech.,8, No. 6, 957–965 (1959).

    MathSciNet  Google Scholar 

  7. A. B. Givental, “Sturm's theorem for hyperelliptic integrals,” Algebra Analiz,1, No. 5, 95–102 (1989).

    MathSciNet  Google Scholar 

  8. A. B. Givental, “Nonlinear generalization of the Maslov index,” Adv. Sov. Math., Vol.1, 1990, pp. 71–103.

    MATH  MathSciNet  Google Scholar 

  9. V. B. Lidskii, “Oscillation theorems for canonical system of differential equations,” Dokl. Akad. Nauk SSSR,105, No. 5, 877–880 (1955).

    MathSciNet  Google Scholar 

  10. M. Morse, “A generalization of the Sturm theorems inn-space,” Math. Ann.,103, 52–69 (1930).

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Morse, “The calculus of variation in the large,” In: AMS Coll. Publ., Vol. 18, New York, 1934, pp. 80–106.

  12. J. Robbin and D. Salamon, “The Maslov index for paths,” Topology,32, No. 4, 827–844 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  13. C. Sturm, “Memoire sur les equaitions differentielles du second ordre,” J. Math. Pures Appl.,1, 106–186 (1836).

    Google Scholar 

  14. A. G. Khovanskii, “Analogues of Aleksandrov-Fenchel inequalities for hyperbolic forms,” Dokl. Akad. Nauk SSSR,276, No. 6, 1332–1334 (1984).

    MATH  MathSciNet  Google Scholar 

  15. V. A. Yakubovich, “Arguments on the group of symplectic matrices,” Mat. Sb.,55, No. 3, 255–280 (1961).

    MATH  MathSciNet  Google Scholar 

  16. V. A. Yakubovich, “Oscillatory properties of solutions of canonical equations,” Mat. Sb.,56, No. 1, 3–42 (1962).

    MATH  MathSciNet  Google Scholar 

  17. V. A. Yakubovich, “Nonoscillation of linear periodic Hamiltonian equations and related problems,” Algebra Analiz,3, No. 5, 229–253 (1991).

    MATH  MathSciNet  Google Scholar 

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Authors
  1. P. E. Pushkar'
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Additional information

The research was partially supported by INTAS grant No. 96-0713 and RFBR grant No. 96-01-01104.

M. V. Lomonosov Moscow State University, Department of Mechanics and Mathematics. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 32, No. 3, pp. 35–49, July–September, 1998.

Translated by P. E. Pushkar'

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Pushkar', P.E. Maslov index and symplectic sturm theorems. Funct Anal Its Appl 32, 172–182 (1998). https://doi.org/10.1007/BF02463338

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