INVARIANT VOLUME FORMS OF GEODESIC, POTENTIAL, AND DISSIPATIVE SYSTEMS ON A TANGENT BUNDLE OF A FOUR-DIMENSIONAL MANIFOLD

Abstract

Complete set of invariant differential forms of phase volume for homogeneous dynamical systems on tangent bundles to smooth four-dimensional manifolds are presented in this paper. The connection between the presence of these invariants and the complete set of the first integrals which are necessary for the integration of geodesic, potential and dissipative systems is shown. At the same time, the introduced force fields make the considered systems dissipative with dissipation of different signs and generalize the previously considered ones.