The Mixmaster cosmology as a dynamical system

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Abstract
The Bianchi IX Mixmaster cosmology is treated as a non-linear dynamical system and the entire spectrum of Lyapunov exponents is calculated from a numerical integration of the full Einstein equations. The behaviour of the solutions is studied for times close to the initial and final singularities as well as for times near the point of maximum expansion. It is demonstrated that the methods of numerical integration must be chosen carefully if a vacuum spacetime is to be simulated in a self-consistent manner. In addition it is shown that previous results pointing to chaotic behaviour are due to inaccurate numerical methods and/or the introduction of non-vacuum behaviour.