PAINLEVE SINGULARITY ANALYSIS OF THE PERFECT FLUID BIANCHI TYPE-IX RELATIVISTIC COSMOLOGICAL MODEL

We perform the Painleve test (i.e. the Kowalevskaya-Gambier test or th e perturbative test) for the perfect fluid Bianchi type-IX relativisti c cosmological model, in order to predict some probable chaotic regime s. This technique enables us to detect every single-valued particular solution associated with a given relativistic dynamical system. Severa l physically interesting cases are studied. These include radiation-do minated and matter-dominated universes, the case of a cosmological con stant and the case of the so-called stiff-matter. In all cases but the cosmological constant case, the models studied do not pass the Painle ve test, exhibit infinitely many movable logarithms and are therefore probably chaotic. Moreover, we show that some physically interesting s ingle-valued particular solutions present in the vacuum case cannot su bsist for a perfect fluid cosmological model. In particular, in the ra diation and dust cases, we show that there cannot exist any exact and closed-form axisymmetric solution.