A pair of an even-dimensional manifold and a non-degenerate closed 2-form on it is called a symplectic manifold. Hamiltonian vector fields are determined for functions on symplectic manifolds, and the study of their periodic solutions occupies a large place in symplectic geometry.
In this talk, we start from the basics of symplectic manifolds and define an invariant called Hofer-Zehnder capacity from the information of periodic solutions of Hamiltonian vector fields. This is an invariant for subsets of symplectic manifolds, and is a kind of what is more commonly called symplectic capacity. We will also discuss some of its applications.
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