ABSTRACT
The state of a system of finitely many particles is described by the probability distri bution function defined on the phase space of the system. The time evolution of the state is determined as a solution of the Cauchy problem for the Liouville equation. The Liouville equation is a first-order partial differential equation. Its solution can be constructed with the help of the solutions of characteristic (Hamiltonian) equations. This is why we first consider the Hamiltonian dynamics of a system of finitely many particles. It is then used for the investigation of statistical systems.
