The order of chaos on a Bianchi-IX cosmological model

The purpose of this paper is to analyze the chaotic behavior that can arise on a type-IX cosmological model using methods from dynamic systems theory and symbolic dynamics. Specifically, instead of the Belinski-Khalatnikov-Lifschitz model, we use the iterates of a monotonously increasing map of the circle with a discontinuity, and for the Hamiltonean dynamics of Misner's Mixmaster model we introduce the iterates of a noninvertible map. An equivalence between these two models can easily be brought upon by translating them in symbolic-dynamical terms. The resulting symbolic orbits can be inserted in an ordered tree structure set, and so we can present an effective counting and referentation of all period orbits.