KNOTS AND LINKS IN INTEGRABLE HAMILTONIAN-SYSTEMS

The main purpose of this paper is to prove that Bott integrable Hamilt onian flows and non-singular Morse-Smale flows are closely related. As a consequence, we obtain a classification of the knots and links form ed by periodic orbits of Bott integrable Hamiltonians on the 3-sphere and on the solid torus. We also show that most of Fomenko's theory on the topology of the energy levels of Bott integrable Hamiltonians can be derived from Morgan's results on 3-manifolds that admit nonsingular Morse-Smale hows.