Conservation laws for classical particles in anti-de Sitter–Beltrami space

The behavior of free classical pointlike particles is governed by conservation laws in the anti-de Sitter space. We present the general form of these laws and their realization in the Beltrami coordinates. In these coordinates, we can pass to the nonrelativistic limit resulting in physics in the $R$ space. We construct the initial covariant distribution function for an ideal gas uniformly filling the entire $R$ space.