  We study a class of dynamical systems for which the motions can be described
in terms of geodesics on a manifold (ordinary potential models can be cast into
this form by means of a conformal map). It is rigorously proven that the
geodesic deviation equation of Jacobi, constructed with a second covariant
derivative, is unitarily equivalent to that of a parametric harmonic
oscillator, and we study the second quatization of this oscillator. The
excitations of the Fock space modes correspond to the emission and absorption
of quanta into the dynamical medium, thus associating unstable behavior of the
dynamical system with calculable fluctuations in an ensamble with possible
thermodynamic consequences.
