Perturbed closed geodesics are periodic orbits: Index and transversality

Mathematische Zeitschrift

Volumn 241, Issue 1, 2002, Pages 45-81

  Weber, Joa ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036026221     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002090100406     Document Type: Article

References (20)

1. [Br83] H. Brezis, Analyse fonctionelle - Thèorie et applications, Masson, Paris, 1983
2. [Ci94] K. Cieliebak, Pseudo-holomorphic curves and periodic orbits on cotangent bundles, J. Math. Pures Appl. 73 (1994), 251-278.
3. [CZ84] C. Conley, E. Zehnder, Morse-type index theory for flows and periodic solutions for hamiltonian equations, Comm. Pure Appl. Math. XXXVII (1984), 207-253
4. [DS94] S. Dostoglou, D.A. Salamon, Cauchy-Riemann operators, self-duality, and the spectral flow, In: First European Congress of Mathematics I, Invited Lectures (Part 1, Eds: A. Joseph, F. Mignot, F. Murat, B. Prum, R. Rentschler), Birkhäuser, Progress in Mathematics 119 (1994), 511-545
5. [Du76] J.J. Duistermaat, On the Morse index in variational calculus, Advances in Math. 21 (1976), 173-195
6. [Fl89] A. Floer, Symplectic fixed points and holomorphic spheres, Commun. Math. Phys. 120 (1989), 575-611
7. [GL58] I.M. Gelfand, V.B. Lidskii, On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients, Translations A.M.S. (2)(8) (1958), 143-181
8. [Hi76] M.W. Hirsch, Differential topology, Graduate Texts in Math. 33, Springer: New York, 1976
9. [RS80] M. Reed, B. Simon, Methods of modern mathematical physics, I Functional analysis, Academic Press, 1980
10. [RS93] J. Robbin, D.A. Salamon, The Maslov index for paths, Topology 32 (1993), 827-844
11. [RS95] J. Robbin, D.A. Salamon, The spectral flow and the Maslov index, Bull. London Math. Soc. 27 (1995), 1-33
12. [Sa96] D.A. Salamon, Spin geometry and Seiberg-Witten invariants, preliminary version June 1996
13. [Sa99] D.A. Salamon, Lectures on Floer Homology, In: Symplectic Geometry and Topology (Eds: Eliashberg, Traynor), IAS/Park City Mathematics series 7 (1999), 143-230
14. [Sm73] S. Smale, An infinite dimensional version of Sard's theorem, Am. J. Math. 87 (1973), 213-221
15. [SW02] D.A. Salamon, J. Weber, J-holomorphic curves in cotangent bundles and Morse theory on the loop space, in preparation
16. [Vi90] C. Viterbo, A new obstruction to embedding Lagrangian tori, Invent. Math. 100(2) (1990), 301-320
17. [Vi94] C. Viterbo, Generating functions, symplectic geometry, and applications, In: Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994). Birkhäuser, Basel (1995), pp. 537-547
18. [Vi96] C. Viterbo, Functors and computations in Floer homology with applications, Part II, Preprint October 1996, revised February 1998
19. [We99] J. Weber, J-holomorphic curves in cotangent bundles and the heat flow, Dissertation TU Berlin, 1999
20. [We02] J. Weber, Geodesic homology, in preparation