## ABSTRACT

We have already discussed the theory of the classication of integrable Hamiltonian

systems with two degrees of freedom up to homeo-and dieomorphisms preserving

trajectories. The main idea of this theory can be brie y formulated in the following

way. Consider two integrable Hamiltonian systems with two degrees of freedom

v

and v

restricted to their regular compact isoenergy submanifolds Q

and Q

.

It is assumed that these systems satisfy some natural conditions. We shall not list

them here, referring the reader to Chapters 3{8, and pointing out that most known

integrable Hamiltonian systems satisfy these conditions. In [46], [53] we have

described complete sets of invariants which allow one to compare the dynamical

systems (v