Perturbation of periodic manifolds of hamiltonian systems
HTML articles powered by AMS MathViewer
- by Alan Weinstein PDF
- Bull. Amer. Math. Soc. 77 (1971), 814-818
References
-
1. R. Abraham and J. Marsden, Foundations of mechanics, Benjamin, New York, 1967. MR 36 #3527.
- Raoul Bott, Nondegenerate critical manifolds, Ann. of Math. (2) 60 (1954), 248–261. MR 64399, DOI 10.2307/1969631
- K. R. Meyer, Generic bifurcation of periodic points, Trans. Amer. Math. Soc. 149 (1970), 95–107. MR 259289, DOI 10.1090/S0002-9947-1970-0259289-X
- J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Comm. Pure Appl. Math. 23 (1970), 609–636. MR 269931, DOI 10.1002/cpa.3160230406 5. H. Poincaré, Les méthodes nouvelles de la mécanique céleste. Tome 1. Solutions périodiques. Non-existence des intégrales uniformes. Solutions asymptotiques, Paris, 1892; English transl., NASA TTF-450, National Aeronautics and Space Administration, Washington, D. C., 1967. MR 19, 414; MR 38 #6135a.
- Georges Reeb, Sur un théorème de Seifert sur les trajectoires fermées de certains champs de vecteurs, Internat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 16–21 (French). MR 0149006 7. J. Roels, Extension aux cas résonants d’un théorème de Liapunov sur les mouvements périodiques voisin d’un équilibre, Rapport n°. 33, Inst. Math. Pure Appl., Université Catholique de Louvain, 1969.
- Herbert Seifert, Closed integral curves in $3$-space and isotopic two-dimensional deformations, Proc. Amer. Math. Soc. 1 (1950), 287–302. MR 37508, DOI 10.1090/S0002-9939-1950-0037508-5
- Alan Weinstein, Symplectic structures on Banach manifolds, Bull. Amer. Math. Soc. 75 (1969), 1040–1041. MR 245052, DOI 10.1090/S0002-9904-1969-12353-0
- Alan Weinstein, Symplectic manifolds and their Lagrangian submanifolds, Advances in Math. 6 (1971), 329–346 (1971). MR 286137, DOI 10.1016/0001-8708(71)90020-X 11. A. Weinstein, Periodic orbits of hamiltonian systems via critical point theory, Preprint, Berkeley, Calif., 1971.
Additional Information
- Journal: Bull. Amer. Math. Soc. 77 (1971), 814-818
- MSC (1970): Primary 7034, 5750
- DOI: https://doi.org/10.1090/S0002-9904-1971-12816-1
- MathSciNet review: 0281230