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New generalizations of Poincaré's geometric theorem

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Literature Cited

  1. 1.

    V. I. Arnol'd, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York—Heidelberg—Berlin (1979).

  2. 2.

    V. I. Arnol'd, "Some remarks on flows of linear elements and frames," Dokl. Akad. Nauk SSSR,138, No. 2, 255–257 (1961).

  3. 3.

    V. I. Arnol'd, Singularities of Differentiable Maps [in Russian], Vol. 1, Nauka, Moscow (1982).

  4. 4.

    V. I. Arnol'd and A. B. Givental’, "Symplectic geometry," in: Contemporary Problems of Mathematics. Fundamental Directions, Vol. 4 [in Russian], Itogi Nauki i Tekhniki, VINITI Akad. Nauk SSSR, Moscow (1985), pp. 7–139.

  5. 5.

    A. Banyaga, "Sur la structure du groupe des diffeomorphismes qui preservent une forme symplectique," Comment. Math. Helv.,53, No. 2, 174–227 (1978).

  6. 6.

    A. Banyaga, "The geometry of the flux homomorphism," Preprint Inst. Fourier, Grenoble (1984).

  7. 7.

    C. C. Conley and E. Zehnder, "The Birkhoff—Lewis fixed point theorem and a conjecture of V. I. Arnold," Invent. Math.,73, No. 1, 33–49 (1983).

  8. 8.

    V. V. Kozlov, "Variational calculus in the large and classical mechanics," Usp. Mat. Nauk,40, No. 2, 33–60 (1985).

  9. 9.

    J. Moser, "On the volume elements on a manifold," Trans. Am. Math. Soc.,120, No. 2, 286–294 (1965).

  10. 10.

    N. A. Nikishin, "On fixed points of diffeomorphisms of the two-dimensional sphere which preserve an oriented plane," Funkts. Anal. Prilozhen.,8, No. 1, 84–85 (1974).

  11. 11.

    S. P. Novikov and I. A. Taimanov, "Periodic extremals of multivalued or noneverywhere positive functionals," Dokl. Akad. Nauk SSSR,274, No. 1, 26–28 (1984).

  12. 12.

    J.-C. Sikorav, "Points fixes d'un symplectomorphism homologue à l'identite," Preprint F-91405-Orsay, Univ. de Paris (1984).

  13. 13.

    C. Simon, "A bound for fixed-point index for an area preserving map with application to mechanics," Invent. Math.,26, No. 2, 187–200 (1974).

  14. 14.

    I. A. Taimanov, "The principle of throwing-out cycles in the Morse—Novikov theory," Dokl. Akad. Nauk SSSR,268, No. 1, 46–50 (1983).

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Additional information

Moscow Steel and Alloys Institute. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 21, No. 2, pp. 16–22, April–June, 1987.

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Ginzburg, V.L. New generalizations of Poincaré's geometric theorem. Funct Anal Its Appl 21, 100–106 (1987).

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  • Functional Analysis
  • Geometric Theorem