Analytic structure and chaos in Bianchi type-IX relativistic dynamics

Using both exact and numerical tools, we show that the analytic structure of SO(3)-invariant spatially homogeneous relativistic dynamics precisely confirms the reliability of discrete mappings due to Belinskij, Khalatnikov and Lifchitz. We propose a strategy in order to tackle chaotic issues in covariant frameworks. Ricci-flat Euclidean metrics as well as minimally coupled scalar field and non-viscous fluid Universe models are then worked out as privileged examples of either quiescent or chaotic systems, thus clearly showing that local Painlevé analysis is necessary but not sufficient in order to decide about chaos.