Volume 5, issue 2 (2001)

Download this article
For printing
Recent Issues

Volume 22
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Hofer–Zehnder capacity and length minimizing Hamiltonian paths

Dusa McDuff and Jennifer Slimowitz

Geometry & Topology 5 (2001) 799–830
Bibliography
1 M Abreu, D McDuff, Topology of symplectomorphism groups of rational ruled surfaces, J. Amer. Math. Soc. 13 (2000) 971 MR1775741
2 M Bialy, L Polterovich, Geodesics of Hofer's metric on the group of Hamiltonian diffeomorphisms, Duke Math. J. 76 (1994) 273 MR1301192
3 M Entov, $K$–area, Hofer metric and geometry of conjugacy classes in Lie groups, Invent. Math. 146 (2001) 93 MR1859019
4 A Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989) 575 MR987770
5 A Floer, H Hofer, D Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995) 251 MR1360618
6 M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
7 H Hofer, Estimates for the energy of a symplectic map, Comment. Math. Helv. 68 (1993) 48 MR1201201
8 H Hofer, C Viterbo, The Weinstein conjecture in the presence of holomorphic spheres, Comm. Pure Appl. Math. 45 (1992) 583 MR1162367
9 H Hofer, E Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag (1994) MR1306732
10 F Lalonde, D McDuff, Hofer's $L^\infty$–geometry: energy and stability of Hamiltonian flows I, II, Invent. Math. 122 (1995) 1, 35 MR1354953
11 G Liu, G Tian, Weinstein conjecture and GW invariants, Commun. Contemp. Math. 2 (2000) 405 MR1806943
12 G Liu, G Tian, Floer homology and Arnold conjecture, J. Differential Geom. 49 (1998) 1 MR1642105
13 G Liu, G Tian, On the equivalence of multiplicative structures in Floer homology and quantum homology, Acta Math. Sin. $($Engl. Ser.$)$ 15 (1999) 53 MR1701133
14 G Lu, The Weinstein conjecture on some symplectic manifolds containing the holomorphic spheres, Kyushu J. Math. 52 (1998) 331 MR1645455
15 D McDuff, The virtual moduli cycle, from: "Northern California Symplectic Geometry Seminar", Amer. Math. Soc. Transl. Ser. 2 196, Amer. Math. Soc. (1999) 73 MR1736215
16 D McDuff, Quantum homology of fibrations over $S^2$, Internat. J. Math. 11 (2000) 665 MR1780735
17 D McDuff, D Salamon, Introduction to symplectic topology, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press (1998) MR1698616
18 D McDuff, D Salamon, $J$–holomorphic curves and quantum cohomology, University Lecture Series 6, American Mathematical Society (1994) MR1286255
19 D McDuff, S Tolman, Topological properties of Hamiltonian circle actions, IMRP Int. Math. Res. Pap. (2006) 72826, 1 MR2210662
20 J Moser, Addendum to: “Periodic orbits near an equilibrium and a theorem by Alan Weinstein”, Comm. Pure Appl. Math. 31 (1978) 529 MR0467821
21 S Piunikhin, D Salamon, M Schwarz, Symplectic Floer–Donaldson theory and quantum cohomology, from: "Contact and symplectic geometry (Cambridge, 1994)", Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 171 MR1432464
22 L Polterovich, Gromov's $K$–area and symplectic rigidity, Geom. Funct. Anal. 6 (1996) 726 MR1406671
23 L Polterovich, Hamiltonian loops and Arnold's principle, from: "Topics in singularity theory", Amer. Math. Soc. Transl. Ser. 2 180, Amer. Math. Soc. (1997) 181 MR1767123
24 L Polterovich, Symplectic aspects of the first eigenvalue, J. Reine Angew. Math. 502 (1998) 1 MR1647622
25 L Polterovich, The geometry of the group of symplectic diffeomorphisms, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag (2001) MR1826128
26 D Salamon, E Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992) 1303 MR1181727
27 M Schwarz, On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193 (2000) 419 MR1755825
28 C L Siegel, J K Moser, Lectures on celestial mechanics, Die Grundlehren der mathematischen Wissenschaften 187, Springer (1971) MR0502448
29 K F Siburg, New minimal geodesics in the group of symplectic diffeomorphisms, Calc. Var. Partial Differential Equations 3 (1995) 299 MR1385290
30 J Slimowitz, PhD thesis, Stony Brook (1998)
31 I Ustilovsky, Conjugate points on geodesics of Hofer's metric, Differential Geom. Appl. 6 (1996) 327 MR1422339
32 A Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math. 20 (1973) 47 MR0328222