On bounded and unbounded dynamics of the Hamiltonian system for unified scalar field cosmology

•Unbounded dynamics is stated in case of negative curvature.•Domain with unbounded dynamics is got in case of positive curvature.•Localization polytope for compact invariant sets is computed.•One two dimensional invariant plane is described.•Nonchaotic dynamics is stated in one special case.

This paper is devoted to the research of global dynamics for the Hamiltonian system formed by the unified scalar field cosmology. We prove that this system possesses only unbounded dynamics in the space of negative curvature. It is found the invariant domain filled only by unbounded dynamics for the space with positive curvature. Further, we construct a set of polytopes depending on the Hamiltonian level surface that contain all compact invariant sets. Besides, one invariant two dimensional plane is described. Finally, we establish nonchaoticity of dynamics in one special case.