Symplectic invariants and Hamiltonian dynamics

There is a mysterious relation between rigidity phenomena of symplectic geometry and global periodic solutions of Hamiltonian dynamics. One of the links is provided by a special class of symplectic invariants discovered by I. Ekeland and H. Hofer in [2], [3] called symplectic capacities. We first recall this concept in a more general setting from [26] and consider the class of all symplectic manifolds (M, ω) possibly with boundary, but of fixed dimension 2n. Here ω is a symplectic structure, i.e. a two-form on M which is closed and nondegenerate.