Poisson brackets and symplectic invariants

Mathematics – Symplectic Geometry

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Scientific paper

We introduce new invariants associated to collections of compact subsets of a
symplectic manifold. They are defined through an elementary-looking variational
problem involving Poisson brackets. The proof of the non-triviality of these
invariants involves various flavors of Floer theory. We present applications to
approximation theory on symplectic manifolds and to Hamiltonian dynamics.

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