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
