Localizing bounds for compact invariant sets of nonlinear systems possessing first integrals with applications to hamiltonian systems

In this paper, we study the localization problem of compact invariant sets of nonlinear systems possessing first integrals by using the first order extremum conditions and positive definite polynomials. In the case of natural polynomial Hamiltonian systems, our results include those in [Starkov, 2008] as a special case. This paper discusses the application to studies of the generalized YangMills Hamiltonian system and the Hamiltonian system describing dynamics of hydrogenic atoms in external fields.