On reversibility in systems with a non-compact configuration space and non-negative potential energy

The problem of the reversibility of the trajectories of a reversible mechanical system with a non-compact configuration space is discussed. To identify the conditions of reversibility in systems with a non-negative potential energy, an invariant Gibbs measure is used. Despite the non-compactness, the Gibbs measure of the entire phase space can be finite, which guarantees reversibility of almost all phase trajectories. Sufficient conditions for reversibility of trajectories of systems with a homogeneous, non-negative potential energy are indicated. As a consequence, reversibility of almost all phase trajectories of the Yang-Mills Hamiltonian with three degrees of freedom is established.