Periodic Trajectories and Topology of the Integrable Boltzmann System (2307.04991v2)

Abstract: We consider the Boltzmann system corresponding to the motion of a billiard with a linear boundary under the influence of a gravitational field. We derive analytic conditions of Cayley's type for periodicity of its trajectories and provide geometric descriptions of caustics. The topology of the phase space is discussed using Fomenko graphs.