Geometrical Aspects of the Hamiltonization Problem of Dynamical Systems

Some positive answers to the problem of endowing a dynamical system with Hamiltonian formulation are presented within class Poisson structures in geometric framework. We address this on orientable manifolds and by using decomposable structures. In first case, existence is ensured under vanishing some topological obstructions, improving result Gao. second we apply variant Hojman construction solve for vector fields admitting transversally invariant metric and, particular, infinitesimal generators proper actions. Finally, also consider hamiltonization Lie group actions give solutions particular case which acting low-dimensional torus.