Localizing bounds and the nonexistence conditions for compact invariant sets of some Hamiltonian systems
In this work we consider three Hamiltonian systems and present results concerning localization bounds and the nonexistence conditions of compact invariant sets. The first two systems are Hamiltonian systems appeared in cosmological studies; they are defined by the conformally/minimally coupled field. Mainly, some nonexistence conditions of compact invariant sets are presented. The third system is a Hamiltonian system with a cubic potential and two degrees of freedom. We give conditions of the existence of a polytope containing all compact invariant sets and, briefly, describe how to compute its bounds.