Symplectic topology and Hamiltonian dynamics. (English) Zbl 0641.53035

In this paper we construct, using variational methods for Hamiltonian systems, a map which associates to every subset of a symplectic vector space a number, called the symplectic capacity of the set. This map is characterized by three axioms. We show that on the smooth level capacity preserving maps are symplectic or antisymplectic. This allows to prove certain new symplectic rigidity results as well as to introduce the notion of a symplectic homeomorphism.
Reviewer: I.Ekeland


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
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