Linearization of Hamiltonian systems through state immersion

This paper deals with the linearization of non-linear Hamiltonian systems through state immersion: under the existence of a suitable symmetry (not necessarily Hamiltonian) of the Hamiltonian system, this is achieved first by linearizing the symmetry through a canonical diffeomorphism, which simultaneously brings the Hamiltonian system into a homogeneous form of degree 0 with respect to a certain dilation and, secondly, by immersing such homogeneous Hamiltonian system into a linear one. This has some direct consequences: the computation in closed form of the flow of the Hamiltonian system and the computation in closed form of the semi-invariants of the system.