First integrals of Hamiltonian systems: the inverse problem (Q827483)

The paper is devoted to an inverse problem defined by checking whether or not a first integral of a Hamiltonian system comes from a Hamiltonian operator (and in finding such Hamiltonian operator) in four distinct cases: three specific Hamiltonian systems (with specific first integrals) from Economics, and one specific Hamiltonian system from Mechanics. There is no general theory in action here and the authors work ``case-by-case''.