Horseshoes and invariant tori in cosmological models with a coupled field and non-zero curvature

Abstract

This paper studies the dynamics of a family of hamiltonian systems that originate from Friedman-Lema\^itre-Robertson-Walker space-times with a coupled field and non-zero curvature. In four distinct cases, previously considered by Maciejewski, Przybylska, Stachowiak & Szydowski, it is shown that there are homoclinic connections to invariant submanifolds and the connections split. These results imply the non-existence of a real-analytic integral independent of the hamiltonian.