We apply the periodic orbit expansion to the calculation of transport,
thermodynamic. and chaotic properties of the finite-horizon triangula
r Lorentz gas. We show numerically that the inverse of the normalized
Lyapunov number is a good estimate of the probability of an individual
periodic orbit. We investigate the convergence of the periodic orbit
expansion and compare it with the convergence of the cycle expansions
obtained from the Ruelle dynamical zeta-function. For this system with
severe pruning we find that applying standard convergence acceleratio
n schemes to the periodic orbit expansion is superior to the dynamical
zeta-function approach. The averages obtained from the periodic orbit
expansion are within 8% of the values obtained from direct numerical
time and ensemble averaging. None of the periodic orbit expansions use
d here is computationally competitive with the standard simulation app
roaches for calculating averages. However, we believe that these expan
sion methods are of fundamental importance, because they give a direct
route to the phase space distribution function.