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 $(N,{\omega }_N)$ 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.

arXiv comment24 pages, 6 figures

References in corpus (5)

• Functors and Computations in Floer homology with Applications Part II
• Noncontractible periodic orbits in cotangent bundles and Floer homology
• Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on $T^*\T^n$ with application to non convex Hamiltonian systems
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Cited by in corpus (3)

• Floer homology in the cotangent bundle of a closed Finsler manifold and noncontractible periodic orbits
• Symplectic deformations of Floer homology and non-contractible periodic orbits in twisted disc bundles
• Non-contractible orbits for Hamiltonian functions on Riemann surfaces