The symplectic topology of completely integrable Hamiltonian systems

Abstract

CONTENTS § 1. Introduction § 2. Necessary definitions § 3. The symplectic topology of Hamiltonian systems (on four-dimensional symplectic manifolds) that are integrable in the class of Bott integrals § 4. The multi-dimensional case. The topological classification of bifurcations of Liouville tori in systems with Bott integrals § 5. Topological invariants of systems that are integrable by means of Bott integrals § 6. The general topological properties of Hamiltonian systems of differential equations that are integrable by means of Bott integrals References