Horseshoes and invariant tori in cosmological models with a coupled field and non-zero curvature * *Partially supported by the Natural Science and Engineering Research Council of Canada Grant 320 852.

Abstract

This paper studies the dynamics of a family of Hamiltonian systems that originate from Friedman–Lemaître–Robertson–Walker space-times with a coupled field and non-zero curvature. In four distinct cases, previously considered by Maciejewski, Przybylska, Stachowiak and 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.