EVIDENCE OF A NATURAL BOUNDARY AND NONINTEGRABILITY OF THE MIXMASTER UNIVERSE MODEL

The formal asymptotic analysis of Latifi et al. [4] suggests that the Mixmaster Universe model possesses movable transcendental singularitie s and thus is nonintegrable in the sense that it does not satisfy the Painleve property (i.e., singularities with nonalgebraic branching). I n this paper, we present numerical evidence of the nonintegrability of the Mixmaster model by studying the singularity patterns in the compl ex t-plane, where t is the ''physical'' time, as well as in the comple x tau-plane, where tau is the associated ''logarithmic'' time. More sp ecifically, we show that in the tau-plane there appears to exist a ''n atural boundary'' of remarkably intricate structure. This boundary lie s at the ends of a sequence of smaller and smaller ''chimneys'' and co nsists of the type of singularities studied in [4], on which pole-like singularities accumulate densely. We also show numerically that in th e complex t-plane there appear to exist complicated, dense singularity patterns and infinitely-sheeted solutions with sensitive dependence o n initial conditions.