Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories

Morimichi Kawasaki, Ryuma Orita
Journal of Modern Dynamics, vol. 11 (2017), pp. 313–339
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Abstract

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The first author introduced a relative symplectic capacity $C$ for a symplectic manifold $(N,\omega_N)$ and its subset $X$ which measures the existence of non-contractible periodic trajectories of Hamiltonian isotopies on the product of $N$ with the annulus $A_R=(-R,R)\times\mathbb{R}/\mathbb{Z}$. In the present paper, we give an exact computation of the capacity $C$ of the $2n$-torus $\mathbb{T}^{2n}$ relative to a Lagrangian submanifold $\mathbb{T}^n$ which implies the existence of non-contractible Hamiltonian periodic trajectories on $A_R\times\mathbb{T}^{2n}$. Moreover, we give a lower bound on the number of such trajectories.

@article{kawasaki2017computation,
  author        = {Kawasaki, Morimichi and Orita, Ryuma},
  title         = {{Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories}},
  journal       = {Journal of Modern Dynamics},
  volume        = {11},
  pages         = {313--339},
  year          = {2017},
  doi           = {10.3934/jmd.2017013},
  eprint        = {1703.01730},
  archivePrefix = {arXiv}
}