Geometric `tempus' for a class of ergodic classical systems

Abstract

Using the symplectic formalism of classical mechanics, a smooth holonomy effect is identified in a special class of classical ergodic Hamiltonian systems (generalized canonical families) that are cycled adiabatically. It is a smooth shift in a time-resembling observable `tempus' that is canonically conjugated to the phase space volume contained in the energy shell. The curvature 2-form of the adiabatic connection obtained is closely related to Hannay's and the Robbins - Berry 2-form. The measurability of the `tempus' is discussed.