THE LAST REMAKE OF THE MIXMASTER UNIVERSE MODEL

We review the existing evidence on the (non)integrability of the mixmaster universe model. We show how a local Painleve analysis can be used to study the possible existence of essential singularities. In agreement with recent studies, we find that the mixmaster model possesses critical essential singularities, the multivalued character of which is incompatible with integrability. Our analysis is complemented by a numerical study of the spectrum of the stretching numbers of the system. We show that the zero-energy case is characterized by a vanishing maximal Lyapunov characteristic number.