Distribution de Boltzmann discrete sur un fibre tangent. (Discrete Boltzmann distribution on a tangent bundle) (Q1115748)

The Boltzmann equation, in classical theory as well as in relativistic theory, may be obtained by studying the molecular chaos propagation which uses a formulation in terms of distributions. In this formulation a linear operator H on the ``TESTS'' functions space occurs and the choice of H determines the nature of the considered theory: continuous or discrete. In this article, we study more specially the discrete case and we prove that the resolution of the Boltzmann equation is brought back to the one of a first order partial derivative equations system on a manifold. To illustrate these results, we develop two simple cases: the case where the manifold is the flat space \({\mathbb{R}}^ 2\) and the one where the manifold is Poincaré's half plane.