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Action and index spectra and periodic orbits in Hamiltonian dynamics

Viktor L Ginzburg and Başak Z Gürel

Geometry & Topology 13 (2009) 2745–2805
Bibliography
1 P Albers, A note on local Floer homology arXiv:math.SG/0606600
2 M Audin, J Lafontaine, editors, Holomorphic curves in symplectic geometry, Progress in Math. 117, Birkhäuser Verlag (1994) MR1274923
3 J F Barraud, O Cornea, Lagrangian intersections and the Serre spectral sequence, Ann. of Math. $(2)$ 166 (2007) 657 MR2373371
4 P Biran, L Polterovich, D Salamon, Propagation in Hamiltonian dynamics and relative symplectic homology, Duke Math. J. 119 (2003) 65 MR1991647
5 Y V Chekanov, Hofer's symplectic energy and Lagrangian intersections, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 296 MR1432467
6 K Cieliebak, V L Ginzburg, E Kerman, Symplectic homology and periodic orbits near symplectic submanifolds, Comment. Math. Helv. 79 (2004) 554 MR2081726
7 C C Conley, Lecture (1984)
8 M Entov, K-area, Hofer metric and geometry of conjugacy classes in Lie groups, Invent. Math. 146 (2001) 93 MR1859019
9 M Entov, L Polterovich, Rigid subsets of symplectic manifolds arXiv:0704.0105
10 M Entov, L Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not. (2003) 1635 MR1979584
11 A Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988) 513 MR965228
12 A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775 MR948771
13 A Floer, Cuplength estimates on Lagrangian intersections, Comm. Pure Appl. Math. 42 (1989) 335 MR990135
14 A Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989) 575 MR987770
15 A Floer, Witten's complex and infinite-dimensional Morse theory, J. Differential Geom. 30 (1989) 207 MR1001276
16 B Fortune, A symplectic fixed point theorem for $\mathbf{C}\mathrm{P}^n$, Invent. Math. 81 (1985) 29 MR796189
17 B Fortune, A Weinstein, A symplectic fixed point theorem for complex projective spaces, Bull. Amer. Math. Soc. $($N.S.$)$ 12 (1985) 128 MR766969
18 J Franks, M Handel, Periodic points of Hamiltonian surface diffeomorphisms, Geom. Topol. 7 (2003) 713 MR2026545
19 U Frauenfelder, F Schlenk, Hamiltonian dynamics on convex symplectic manifolds, Israel J. Math. 159 (2007) 1 MR2342472
20 V L Ginzburg, The Conley conjecture arXiv:math.SG/0610956
21 V L Ginzburg, The Weinstein conjecture and theorems of nearby and almost existence, from: "The breadth of symplectic and Poisson geometry" (editors J E Marsden, T S Ratiu), Progr. Math. 232, Birkhäuser (2005) 139 MR2103006
22 V L Ginzburg, Coisotropic intersections, Duke Math. J. 140 (2007) 111 MR2355069
23 V L Ginzburg, B Z Gürel, Generic existence of infinitely many periodic orbits in Hamiltonian dynamics, in preparation
24 V L Ginzburg, B Z Gürel, Local Floer homology and the action gap arXiv:0709.4077v2
25 V L Ginzburg, B Z Gürel, Periodic orbits of twisted geodesic flows and the Weinstein–Moser theorem, to appear in Comment. Math. Helv. arXiv:0705.1818
26 V L Ginzburg, B Z Gürel, Relative Hofer–Zehnder capacity and periodic orbits in twisted cotangent bundles, Duke Math. J. 123 (2004) 1 MR2060021
27 V L Ginzburg, E Kerman, Homological resonances for Hamiltonian diffeomorphisms and Reeb flows, Int. Math. Res. Not. (2009)
28 V Guillemin, V L Ginzburg, Y Karshon, Moment maps, cobordisms, and Hamiltonian group actions, Math. Surveys and Monogr. 98, Amer. Math. Soc. (2002) MR1929136
29 B Z Gürel, Totally non-coisotropic displacement and its applications to Hamiltonian dynamics, Commun. Contemp. Math. 10 (2008) 1103 MR2483254
30 N Hingston, Subharmonic solutions of Hamiltonian equations on tori, to appear in Ann. of Math.
31 H Hofer, Lusternik–Schnirelman-theory for Lagrangian intersections, Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988) 465 MR970850
32 H Hofer, D A Salamon, Floer homology and Novikov rings, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 483 MR1362838
33 H Hofer, C Viterbo, The Weinstein conjecture in the presence of holomorphic spheres, Comm. Pure Appl. Math. 45 (1992) 583 MR1162367
34 H Hofer, E Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser Verlag (1994) MR1306732
35 E Kerman, Squeezing in Floer theory and refined Hofer–Zehnder capacities of sets near symplectic submanifolds, Geom. Topol. 9 (2005) 1775 MR2175157
36 E Kerman, Hofer's geometry and Floer theory under the quantum limit, Int. Math. Res. Not. (2008) MR2417790
37 H V Lê, K Ono, Cup-length estimates for symplectic fixed points, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 268 MR1432466
38 G Liu, G Tian, Weinstein conjecture and GW–invariants, Commun. Contemp. Math. 2 (2000) 405 MR1806943
39 G Lu, Gromov–Witten invariants and pseudo symplectic capacities, Israel J. Math. 156 (2006) 1 MR2282367
40 D McDuff, Hamiltonian $S^1$–manifolds are uniruled, Duke Math. J. 146 (2009) 449 MR2484280
41 D McDuff, D Salamon, Introduction to symplectic topology, Oxford Math. Monogr., Oxford Science Publ., The Clarendon Press, Oxford Univ. Press (1995) MR1373431
42 D McDuff, D Salamon, $J$–holomorphic curves and symplectic topology, Amer. Math. Soc. Coll. Publ. 52, Amer. Math. Soc. (2004) MR2045629
43 Y G Oh, A symplectic fixed point theorem on $T^{2n}\times\mathbf{C}\mathrm{P}^k$, Math. Z. 203 (1990) 535 MR1044063
44 Y G Oh, Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds, from: "The breadth of symplectic and Poisson geometry" (editors J E Marsden, T S Ratiu), Progr. Math. 232, Birkhäuser (2005) 525 MR2103018
45 K Ono, On the Arnold conjecture for weakly monotone symplectic manifolds, Invent. Math. 119 (1995) 519 MR1317649
46 Y Ostrover, Calabi quasi-morphisms for some non-monotone symplectic manifolds, Algebr. Geom. Topol. 6 (2006) 405 MR2220683
47 S Piunikhin, D Salamon, M Schwarz, Symplectic Floer-Donaldson theory and quantum cohomology, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 171 MR1432464
48 M Poźniak, Floer homology, Novikov rings and clean intersections, from: "Northern California Symplectic Geometry Seminar" (editors Y Eliashberg, D Fuchs, T Ratiu, A Weinstein), Amer. Math. Soc. Transl. Ser. 2 196, Amer. Math. Soc. (1999) 119 MR1736217
49 D A Salamon, Lectures on Floer homology, from: "Symplectic geometry and topology" (editors Y Eliashberg, L Traynor), IAS/Park City Math. Series 7, Amer. Math. Soc. (1999) MR1702940
50 D A Salamon, E Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992) 1303 MR1181727
51 M Schwarz, A quantum cup-length estimate for symplectic fixed points, Invent. Math. 133 (1998) 353 MR1632778
52 M Schwarz, On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193 (2000) 419 MR1755825
53 A Cannas da Silva, Lectures on symplectic geometry, Lecture Notes in Math. 1764, Springer (2001) MR1853077
54 M Usher, Spectral numbers in Floer theories, Compos. Math. 144 (2008) 1581 MR2474322
55 M Usher, Floer homology in disk bundles and symplectically twisted geodesic flows, J. Mod. Dyn. 3 (2009) 61 MR2481333
56 C Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992) 685 MR1157321
57 C Viterbo, Functors and computations in Floer homology with applications. I, Geom. Funct. Anal. 9 (1999) 985 MR1726235