  We investigate the relationship between the Lyapunov exponents of periodic
trajectories, the average and fluctuations of Lyapunov exponents of ergodic
trajectories, and the ergodic autocorrelation time for the two-dimensional
hyperbola billiard. We then study the fluctuation properties of the ergodic
Lyapunov spectrum of classical SU(2) gauge theory on a lattice. Our results are
consistent with the notion that this system is globally hyperbolic. Among the
many powerful theorems applicable to such systems, we discuss one relating to
the fluctuations in the entropy growth rate.
