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

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