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

Abstract

The first author introduced a relative symplectic capacity C for a symplectic manifold (N,ωN) and its subset X which measures the existence of non-contractible periodic trajectories of Hamiltonian isotopies on the product of N with the annulus AR=(R,R)×R/Z. In the present paper, we give an exact computation of the capacity C of the 2n-torus T2n relative to a Lagrangian submanifold Tn which implies the existence of non-contractible Hamiltonian periodic trajectories on AR×T2n. Moreover, we give a lower bound on the number of such trajectories.

Publication
Journal of Modern Dynamics, vol. 11 (2017), pp. 313–339