CHAOS HIDDEN BEHIND TIME PARAMETRIZATION IN THE MIXMASTER COSMOLOGY

We define the Maupertuis clock which counts Kasner epochs in the Mixma ster cosmology. The characteristic time scale as measured by this cloc k is just the length of a given Kasner epoch. We show that in every tr ansition from one Kasner epoch to another one unit of information is l ost. Relationships of the Maupertuis time with other time parametrizat ions used in general relativity (cosmological time, Misner time, Chitr e-Misner time, curvature time and superspace time) are investigated. I n the logarithmic (mechanical) time nearby trajectories diverge linear ly and the system behaves as if it mere integrable and the chaos is '' hidden'' behind this parametrization. The physical meaning of the Maup ertuis time, as a chaos indicator, is discussed. We also investigate t he dependence of the Lyapunov exponents on time reparametrizations.