Chaos, fractality and topological entropy in cosmological models with a scalar field (Q1609845)

For a Friedmann-Robertson-Walker cosmological model with one real massive scalar field as source, the Einstein field equation yields a system of nonlinear ordinary differential equations. For the closed model a bounce is possible to prevent a big bang. In the present paper, the main emphasis is on the existence of chaotic behaviour in the dynamics. This is non-trivial, because it is not at all easy to prove for a given oscillatory solution that it is not periodic in time with a period being much larger than the time for one oscillation of the scalar field.