ON A POLYTOPE CONTAINING ALL COMPACT INVARIANT SETS FOR A CLASS OF NATURAL POLYNOMIAL HAMILTONIAN SYSTEMS

Abstract

In this paper we give sufficient conditions under which there exists a polytope containing all compact invariant sets for one class of natural polynomial Hamiltonian systems. As an example, we compute bounds of a polytope with this property for a class of natural polynomial Hamiltonian systems with a cubic potential and two degrees of freedom.