On the existence and non-existence of closed trajectories for some Hamiltonian flows

Mathematische Zeitschrift

Volumn 223, Issue 3, 1996, Pages 397-409

  Ginzburg, Viktor L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030294612     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004565     Document Type: Article

References (27)

1. Arnold, V.I.: Some remarks on flows of line elements and frames. Soviet Math. Dokl. 2, 562-564 (1961)
2. Arnold, V.I.: First steps of symplectic topology, Russian Math. Surveys 41(6), 1-21 (1986)
3. Banyaga, A., Rukimbira, Ph.: Weak stability of almost regular contact flows. Preprint
4. Benci, V.: Periodic solutions of Lagrangian systems on a compact manifold. J. Diff. Eq. 63, 135-161 (1986)
5. Conley, C. C., Zehnder, E.: The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold. Invent. Math. 73, 33-49 (1983)
6. Floer, A.: Symplectic fixed points and holomorphic spheres. Commun. Math. Phys. 120, 575-611 (1989)
7. Ginzburg, V.L.: New generalizations of Poincare's geometric theorem. Funct. Anal. Appl. 21(2), 100-106 (1987)
8. Ginzburg, V.L.: On closed characteristics of 2-forms. Russian Math. Surveys 43(2), 225-226 (1988)
9. Ginzburg, V. L.: On closed characteristics of 2-forms. PhD Thesis, Berkeley, 1990
10. Ginzburg, V. L.: Accessible points and closed trajectories of mechanical systems. Preprint, 1993. To appear as an appendix to Global Analysis in Mathematical Physics by Yu. Gliklikh to be published by Springer-Verlag
11. 2n, 2n-1 ≧ 7, whose Hamiltonian flow has no periodic trajectories. IMRN 83-96 (1995) no. 2
12. Hedlund, G.A.: Fuchsian groups and transitive horocycles. Duke Math. J. 2, 530-542 (1936)
13. ∞ n'a d'orbites périodiques sur ouvert de surfaces d'énergies. C.R. Acad. Sci. Paris Sér. I Math. 312, 989-994 (1991)
14. Hofer, H., Salamon, D.: Floer homology and Novikov rings, in the Floer Memorial Volume, H. Hofer, et al. (editors), Birkhäuser, Boston, 1995
15. Hofer H., Viterbo, C.: The Weinstein conjecture for cotangent bundles and related results. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988) no 3 411-445 (1989)
16. Hofer, H., Zehnder, E.: Periodic solution on hypersurfaces and a result by C. Viterbo. Invent. Math. 90, 1-9 (1987)
17. Kuperberg, G.: A volume-preserving counterexample to the Seifert conjecture. Comment. Math. Helvetici 71, 70-97 (1996)
18. McCord C., Oprea, J.: Rational Ljusternik-Schnirelman category and the Arnold's conjecture for nilmanifolds. Topology 32, 701-717 (1993)
19. McDuff, D.: Symplectic manifolds with contact type boundaries. Invent. Math. 103, 651-671 (1991)
20. Novikov, S.P.: The Hamiltonian formalism and many-valued analogue of Morse theory. Russian Math. Surveys 37(5), 1-56 (1982)
21. Novikov, S.P., Taimanov, I.A.: Periodic extremals of many-valued or not-everywhere-positive functionals. Sov. Math. PDokl. 29(1), 18-20 (1984)
22. Tabachnikov, S.L.: Characteristic classes of Lagrangian foliations. Funct. Anal. Appl. 23(2), 162-163 (1989)
23. Taimanov, I.A.: Closed extremals on two-dimensional manifolds. Russian Math. Surveys, 47(2), 163-211 (1992)
24. 2n. Ann. Inst. H. Poincaré, Anal. Non Linéaire 4, 337-356 (1987)
25. Weinstein, A.: On the hypothesis of Rabinowitz' periodic orbit theorem. J. Diff. Eq. 33, 353-358 (1979)
26. 0-perturbation theorem for symplectic fixed points and Lagrangian intersections. Seminaire Sud-Rhodanien de géométrie, III (Lyon, 1983), Traveaux en cours, Paris, Hermann, 140-144 (1984)
27. Zehnder, E.: Remarks on periodic solutions on hypersurfaces, in Periodic solutions of hamiltonian systems and related topics by Rabinowitz et al., Reidel Publishing Co. 267-279 (1987)