NEW CASES OF INTEGRABLE CONSERVATIVE AND DISSIPATIVE SYSTEMS OF ANY ODD ORDER

New cases of integrable dynamical systems of any odd order homogeneous in terms of variables are presented, in which a system on a tangent bundle to a even-dimensional manifold can be distinguished. In this case, the force field (shift generator in the system) is divided into an internal (conservative) and an external one, which has a dissipation of a different sign. The external field is introduced using some unimodular transformation and generalizes the previously considered fields. Complete sets of both first integrals and invariant differential forms are given.