PAINLEVE SINGULARITY ANALYSIS OF THE BRANS-DICKE BIANCHI TYPE-IX VACUUM COSMOLOGICAL MODEL

We perform the Painleve test for the Bianchi type-IX homogeneous geome try studied in the Brans-Dicke theoretical framework and considered in the vacuum case. We show that this spatially homogeneous cosmological dynamics is not integrable in the Painleve sense: the model studied d oes not pass the perturbative Painleve test, exhibits infinitely many movable logarithmic branchings and is therefore probably chaotic, a fa ct supported by some recent numerical investigations. Moreover, this t echnique enables us to detect every single-valued particular solution associated with the dynamics under study, and these particular solutio ns are explicitly written whenever possible.