Periodic orbits in magnetic fields and ricci curvature of lagrangian systems

Transactions of the American Mathematical Society

Volumn 350, Issue 7, 1998, Pages 2697-2717

  Bahri, Abbas ^a   Taimanov, Iskander A ^b  

^a RUTGERS UNIVERSITY   (United States)

^b SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22044436596     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-98-02108-4     Document Type: Article

References (22)

1. [A] Arnold V.l., First steps in symplectic topology, Russian Mathematical Surveys 41 : 6 (1986), 1-21. MR 89d:58034
2. [B] Bahri A., Pseudo-orbits of contact forms, Pitman Research Notes in Mathematics Series. V. 173. Longman Scientific and Technical, 1988. MR 90i:58160
3. [CZ] Conley C., Zehnder E., The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold, Invent. Math. 73 (1983), 33-49. MR 85e:58044
4. [Gl] Ginzburg V.L., New generalizations of the geometrical theorem of Poincaré, Funct. Anal. Appl. 21 (1987), 100-106. MR 89f:58057
5. [G2] Ginzburg V.L., On the existence and non-existence of closed trajectories for some hamiltonian flows, Math. Zeitschrift. 223 (1996), 397-409. MR 971:58144
6. [GN] Grinevich P.G., Novikov S.P., Nonselfintersecting magnetic orbits on the plane. Proof of the overthrowing of cycles principle, Topics in Topology and Mathematical Physics, AMS Translations - Series 2. Vol. 170, 1995, pp. 59-82. MR 9Gj:58031
7. [H] Hedlund G.A., Fuchsian groups and transitive horocycles, Duke Math. J. 2 (1936), 530542.
8. [Kl] Klingenberg, W., Lectures on closed geodesies, Grundlehren Math. Wiss., Bd. 230, Springer, Berlin and New York, 1978. MR 57:17563
9. [K2] Klingenberg, W., Riemannian geometry, 2nd ed., Studies in Math., de Gruter, Berlin and New York, 1995. MR 95m:58003
10. [Ko] Kozlov V.V., Calculus of variations in the large and classical mechanics, Russian Mathematical Surveys 40 : 2 (1985), 37-71. MR 86m:58053
11. Milnor, J., Morse theory, Ann. Math. Studies, no. 51, Princeton Univ. Press, Princeton, N.J., 1963. MR 29:634
12. [Nl] Novikov, S.P., Multivalued functions and functional. An analogue of Morse theory, Soviet Math. Dokl. 24 (1981), 222-226. MR 83a:58025
13. [N2] Novikov, S.P., Variational methods-and periodic solutions of equations of Kirchhoff type. II, Functional Anal. Appl. 15 (1981), 263-274. MR 83a:58026b
14. [N3] Novikov, S.P., Hamiltonian formalism and a multivalued analogue of Morse theory, Russian Math. Surveys 37 : 5 (1982), 1-56. MR 84h:58032
15. [NS] Novikov, S.P., Shmel'tser, I., Periodic solutions of the Kirchhoff equations for the free motion of a rigid body in a liquid, and the extended Lyusternik-Schnirelmann-Morse (LSM) theory.I, Functional Anal. Appl. 15 (1981), 197-207. MR 83a:58026a
16. [NT] Novikov, S.P., Taimanov I.A., Periodic extremals of multivalued or not everywhere positive functionals, Soviet Math. Dokl. 29 (1984), 18-20. MR 85i:58032
17. [PS] Palais, R., Smale, S., A generalized Morse theory, Bull. Amer. Math. Soc. 70 (1964), 165-171. MR 28:1634
18. [SU] Sacks J., Uhlenbeck K., The existence of minimal immersions of two-spheres, Ann. of Math. 113 (1981), 1-24. MR 82f:58035
19. [T1] Taimanov, I.A., The principle of throwing out cycles in Morse-Novikov theory, Soviet Math. Dokl. 27 (1983), 43-46. MR 84h:58038
20. [T2] Taimanov, I.A., Non-selfintersecting closed extremals of multivalued or not everywhere positive functionals, Math. USSR Izvestiya 38 (1992), 359-374. MR 921:58036
21. [T3] Taimanov, I.A., Closed non-selfintersecting extremals of multivalued functionals, Siberian Math. Journal 33 (1992), 686-692. MR 93j:49004
22. [T4] Taimanov, I.A., Closed extremals on two-dimensional manifolds, Russian Math. Surveys 47 : 2 (1992), 163-211. MR 93k:58050