The Mixmaster Model as a Cosmological Framework and Aspects of its Quantum Dynamics

This paper provides a review of some recent issues on the Mixmaster dynamics concerning the features of its stochasticity. After a description of the geometrical structure characterizing the homogeneous cosmological models in the Bianchi classification and the Belinsky-Khalatnikov-Lifshitz piecewise representation of the types VIII and IX oscillatory regime, we face the question regarding the time covariance of the resulting chaos as viewed in terms of continuous Misner-Chitr\'e like variables. Finally we show how in the statistical mechanics framework the Mixmaster chaos raises as semiclassical limit of the quantum dynamics in the Planckian era.