Abstract.Under certain conditions, generalized action-angle coordinates can be introduced near noncompact invariant manifolds of completely and partially integrable Hamiltonian systems.

The Mishchenko-Fomenko theorem on noncommutative completely integrable Hamiltonian systems on a symplectic manifold is extended to the case of noncompact invariant submanifolds.

A time-dependent completely integrable Hamiltonian system is quantized with respect to time-dependent action-angle variables near an instantly compact regular invariant manifold. Its Hamiltonian depends only on action variables, and has a time-independent countable energy spectrum. (C) 2002 American Institute of Physics

The obstruction to the existence of global action-angle coordinates of Abelian and noncommutative (non-Abelian) completely integrable systems with compact invariant submanifolds has been studied. We extend this analysis to the case of noncompact invariant submanifolds.

Abstract. We establish a new version of the first Noether Theorem, according to which the (equivalence classes of) first integrals of given Euler-Lagrange equations in one independent variable are in exact oneto-one correspondence with the (equivalence classes of) vector fields satisfying two simple geometric conditions, namely they simultaneously preserve the holonomy distribution of the jets space and the action from which the Euler-Lagrange equations are derived.