Computation of annular capacity by hamiltonian floer theory of non-contractible periodic trajectories

Abstract

The first author [9] 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. © 2017 AIMSCIENCES