| The
Hamiltonian dynamics is a rich source of problems in symplectic
topology. In fact, the symplectic topology itself has appeared as the
geometrization of several problems having arisen in the Hamiltonian
dynamics. I intend to discuss two problems which I faced with during my
work under the problems in Hamiltonian dynamics, both integrable and nonintegrable. These are interrelations between the topology of the ambient manifold and the topology of the degeneracy set for an integrable Hamiltonian system and counting of self-intersection points for tori in the scattering problems arising in homoclinic dynamics. |