Between symplectic dynamics and symplectic topology.
Abstract. Since symplectic revolution of the 1980-ies we witnessed a fruitful interaction between symplectic topology and symplectic dynamics. In the talk I shall illustrate some aspects of this interaction in a number of examples:
(1) Asymptotic invariants of symplectic maps: Their study uses the Floer theory, a powerful tool of modern symplectic topology.
(2) Function theory on symplectic manifolds: Nowadays this subject is making its first steps. Its surprising feature is appearance of seemingly elementary statements on functions which involve the uniform norm and the Poisson bracket. Their proofs are based on ideas and methods of symplectic dynamics.