A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM

Abstract

A new topological invariant is constructed which classifies integrable Hamiltonian systems with two degrees of freedom (admitting a Bott integral). A criterion for the equivalence of Bott systems is proved: such systems are topologically equivalent if and only if their topological invariants coincide. The topological invariant is effectively calculated for specific integrable Hamiltonian systems in physics and mechanics.