Journal of Modern Dynamics (JMD)

Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories
Pages: 313 - 339, Volume 11, 2017

doi:10.3934/jmd.2017013      Abstract        References        Full text (425.1K)           Related Articles

Morimichi Kawasaki - Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 790-784, Republic of Korea (email)
Ryuma Orita - Graduate School of Mathematical Sciences, University of Tokyo, Tokyo 153-0041, Japan (email)

1 P. Biran, L. Polterovich and D. Salamon, Propagation in Hamiltonian dynamics and relative symplectic homology, Duke Math. J., 119 (2003), 65-118.       
2 K. Cieliebak, Handle attaching in symplectic homology and the chord conjecture, J. Eur. Math. Soc. (JEMS), 4 (2002), 115-142.       
3 K. Cieliebak, A. Floer and H. Hofer, Symplectic homology, II. A general construction, Math. Zeit., 218 (1995), 103-122.       
4 A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys., 120 (1989), 575-611.       
5 A. Floer and H. Hofer, Symplectic homology, I. Open sets in $\mathbbC^n$, Math. Zeit., 215 (1994), 37-88.       
6 A. Floer, H. Hofer and D. Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J., 80 (1995), 251-292.       
7 U. Frauenfelder and F. Schlenk, Hamiltonian dynamics on convex symplectic manifolds, Israel J. Math., 159 (2007), 1-56.       
8 H. Ishiguro, Non-contractible orbits for Hamiltonian functions on Riemann surfaces, arXiv:1612.07062, (2016).
9 M. Kawasaki, Heavy subsets and non-contractible trajectories, arXiv:1606.01964, (2016).
10 C. Niche, Non-contractible periodic orbits of Hamiltonian flows on twisted cotangent bundles, Discrete Contin. Dyn. Syst., 14 (2006), 617-630.       
11 M. Po┼║niak, Floer homology, Novikov rings and clean intersections, in Northern California Symplectic Geometry Seminar (eds. Y. Eliashberg, D. Fuchs, T. Ratiu and A. Weinstein), Amer. Math. Soc. Transl. Ser. 2, 196, Adv. Math. Sci., 45, Amer. Math. Soc., Providence, RI, 1999, 119-181.       
12 D. Salamon, Lectures on Floer homology, in Symplectic Geometry and Topology (Park City, Utah, 1997), IAS/Park City Math. Ser., 7, Amer. Math. Soc., Providence, RI, 1999, 143-229.       
13 D. Salamon and E. Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math., 45 (1992), 1303-1360.       
14 M. Usher, The sharp energy-capacity inequality, Commun. Contemp. Math., 12 (2010), 457-473.       
15 C. Viterbo, Functors and computations in Floer homology with applications. I, Geom. Funct. Anal., 9 (1999), 985-1033.       
16 J. Weber, Noncontractible periodic orbits in cotangent bundles and Floer homology, Duke Math. J., 133 (2006), 527-568.       
17 J. Xue, Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on $T^*\mathbbT^n$ with application to non convex Hamiltonian systems, to appear in J. Symplectic Geom., arXiv:1408.5193, (2014).

Go to top