Reduction of Hamiltonian systems with symmetry (Q1181697)

This interesting paper presents an extension of the Marsden-Weinstein reduction procedure for Hamiltonian systems with symmetry, and gives a control theoretical interpretation of the techniques used. In section 2 the uathor shows how the hypothesis in the usual Marsden- Weinstein result can be weakened. In particular, using a Lie algebra of infinitesimal symmetries instead of a Lie group, the existence of the reduced phase space is proved without recourse to the existence of an equivariant moment mapping. In section 3 it is shown that the reduction process can be viewed as a minimal realization problem for a Hamiltonian control system, ``and the construction now proposed is very close to some of the main ideas in geometrical control theory''. Examples are given in section 4.