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Normal modes for nonlinear hamiltonian systems

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References

  1. Abraham, R., Marsden, J.: Foundations of Mechanics New York: W. A. Benjamin 1967.

    Google Scholar 

  2. Berger, M. S.: Autonomous perturbations of some hamiltonian systems, all of whose solutions are periodic. In: Ordinary Differential Equations, pp. 351–357. New York: Academic Press 1972.

    Google Scholar 

  3. Ganea, T.: Sur quelques invariants numériques du type d'homotopic. Cahiers de Topologie et Géométrie Differentielle9, 181–241 (1967).

    Google Scholar 

  4. Gordon, W. B.: A theorem on the existence of periodic solutions to Hamiltonian systems with convex potential. J. Diff. Eq.10, 324–335 (1971).

    Google Scholar 

  5. Hirzebruch, F., Meyer, K. H.:O(n)-Mannigfaltigkeiten, exotische Sphären und Singularitäten. Lecture Notes in Mathematics57. Berlin-Heidelberg-New York: Springer 1968.

    Google Scholar 

  6. Horn, J.: Beiträge zur Theorie der kleinen Schwingungen. Z. Math. Phys.48, 400–434 (1903).

    Google Scholar 

  7. Krasnosel'skiî, M. A.: On special coverings of a finite dimensional sphere. Dokl. Akad. Nauk. S.S.S.R.103, 961–964 (1955).

    Google Scholar 

  8. Liapounov, M. A.: Problème général de la Stabilité du Mouvement, Princeton: Princeton Univ. Press 375–392 (1949). (Reprinted from Ann. Fac. Sci. Toulouse9 (1907) and an earlier Russian version.)

    Google Scholar 

  9. Lusternik, L., Schnirelman, L.: Méthodes Topologiques dans les problèmes variationels. Paris: Hermann 1934

    Google Scholar 

  10. Moser, J.: Regularization of Kepler's problem and the averaging method on a manifold. Comm. Pure Appl. Math.23, 609–636 (1970).

    Google Scholar 

  11. Robinson, R. C.: Generic properties of conservative systems. Amer. J. Math.92, 562–603 (1970).

    Google Scholar 

  12. Seifert, H.: Periodische Bewegungen mechanischer Systeme. Math. Z.51, 197–216 (1948).

    Google Scholar 

  13. Souriau, J.-M.: Structure des Systèmes Dynamiques. Paris: Dunod 1970.

    Google Scholar 

  14. Weinstein, A.: Perturbation of periodic manifolds of hamiltonian systems. Bull. Amer. Math. Soc.77, 814–818 (1971).

    Google Scholar 

  15. Weinstein, A.: Lagrangian submanifolds and hamiltonian systems. Annals of Math. (To appear.)

  16. Fuller, F. B.: An index of fixed point type for periodic orbits, Amer. J. Math.89, 133–148 (1967).

    Google Scholar 

  17. Meyer, K. R., Schmidt, D. S.: Periodic orbits near ℒ4 for mass ratios near the critical mass ratio of Routh. Celest. Mech.4, 99–109 (1971).

    Google Scholar 

  18. Roels, J.: An extension to resonant cases of Liapunov's theorem concerning the periodic solutions near a Hamiltonian equilibrium. J. Diff. Eq.9, 300–324 (1971).

    Google Scholar 

  19. Siegel, C. L.: Vorlesungen über Himmelsmechanik. Berlin-Göttingen-Heidelberg: Springer 1956.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, Calif., USA

    Alan Weinstein

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  1. Alan Weinstein
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Research supported by NSF Grant GP-34785 and a Sloan Fellowship.

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Weinstein, A. Normal modes for nonlinear hamiltonian systems. Invent Math 20, 47–57 (1973). https://doi.org/10.1007/BF01405263

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  • DOI: https://doi.org/10.1007/BF01405263

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