  In this work we study the existence of mechanisms of transition to global
chaos in a closed Friedmann-Robertson-Walker universe with a massive
conformally coupled scalar field. We propose a complexification of the radius
of the universe so that the global dynamics can be understood. We show
numerically the existence of heteroclinic connections of the unstable and
stable manifolds to periodic orbits associated to the saddle-center equilibrium
points. We find two bifurcations which are crucial in creating non-collapsing
universes both in the real and imaginary version of the models. The techniques
presented here can be employed in any cosmological model.
