Is the Universe a Simple Dynamical System with Complex Behaviour?

Abstract

In the present paper it is demonstrated the existence of complex (chaotic) behaviour in the time evolution of cosmological models.

We demonstrate that it is difficult to determine a precise sense of chaos in the Bianchi IX models. It can only be shown that some of their approximations form the systems with the property of the Bernoulli shifts. On the other hand, there are examples of integrable systems, but their approximations are non-integrable, e.g. the geodesic motion in the truncated to any finite order of Kerr geometry is not integrable and also chaotic. The generalized criterion of chaotic behaviour from the Maupertuis geometry of dynamics is proposed chaotic behaviour from the Maupertuis geometry of dynamics is proposed as a method of invariant chaos description.