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Proof of a generalized from of a fixed point theorem due to G. D. Birkhoff

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Geometry and Topology

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 597))

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References

  1. G. D. Birkhoff, Dynamical Systems, American Mathematical Society, 1966.

    Google Scholar 

  2. Siegel, C. L., and Moser, J., Lectures on Celestial Mechanics, Springer-Verlag, 1971.

    Google Scholar 

  3. Birkhoff, G. D., Une generalization à n-dimensions du dernier théorème de géométrie de Poincaré, Compt. Rend. Acad. Sci. 192, 1931, 196–198.

    MATH  Google Scholar 

  4. Birkhoff, G. D., and Lewis, D. C., On the periodic motions near a given periodic motion of a dynamical system, Annali di Mat. 12, 1933, pp. 117–133.

    Article  MathSciNet  MATH  Google Scholar 

  5. Lewis, D. C., Sulle oscillazioni periodiche d'une sistema dinamico, Atti Accad. Naz. Sincei Rend. Cl. Sci. Fis. Mat. 19, 1934, 234–237.

    MATH  Google Scholar 

  6. Harris, T. C., Periodic solutions of arbitrary long periods in Hamiltonian systems, Jour. Diff. Eq. 4, 1968, 131–141.

    Article  MATH  Google Scholar 

  7. Arnold, V. I., Sur une properiété topologique des applications globalement canonique de la mécanique classique, Comp. Rend. Acad. Sci. 261, 1965, 3719–3722.

    Google Scholar 

  8. Arnold, V. I., and Avez, A., Problèmes ergodiques de la mécanique classique, Gauthiers-Villars, 1967, Appendix 33.

    Google Scholar 

  9. Weinstein, A., Symplectic structures on Banach manifolds, Bull. A.M.S., 1040–1041, 1969.

    Google Scholar 

  10. Moser, J., On the volume elements on a manifold, Trans. Am. Math. Soc. 120, 286–294, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  11. Lanford III, O. E., Bifurcation of periodic solutions into invariant tori; the work of Ruelle and Takens, Lecture Notes in Mathematics 322, 159–192, Springer-Verlag, 1972.

    Google Scholar 

  12. Zehnder, E., Stability and Instability in Celestial Mechanics, Ensciquement du 3e Cycle de la Physique en Suisse Romande, Ecole Polytechnique Federale, Lausanne, 1975, esp. Appendix III.

    Google Scholar 

  13. Fenichel, N., Persistence and smoothness of invariant manifolds for flows, Ind. Univ. Math. Jour. 21, 193–226, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  14. Klingenberg, W., Closed Geodesics on Riemannian manifolds, Proc. 13 Biennial Seminar Canadian Math. Congress. ed. J. R. Vanstone, Montreal, Canada, 1972, Vol. 1, pp. 69–92.

    Google Scholar 

  15. Klingenberg, W., Lectures on Closed Geodesics, (second and revised edition), preprint, University Bonn, 1976.

    Google Scholar 

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, USA

    J. Moser

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  1. J. Moser
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Jacob Palis Manfredo do Carmo

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© 1977 Springer-Verlag

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Moser, J. (1977). Proof of a generalized from of a fixed point theorem due to G. D. Birkhoff. In: Palis, J., do Carmo, M. (eds) Geometry and Topology. Lecture Notes in Mathematics, vol 597. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085372

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  • DOI: https://doi.org/10.1007/BFb0085372

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08345-0

  • Online ISBN: 978-3-540-37301-8

  • eBook Packages: Springer Book Archive

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