  We obtain general predictions for the distribution of wave function
intensities in position space on the periodic orbits of chaotic ballistic
systems. The expressions depend on effective system size N, instability
exponent lambda of the periodic orbit, and proximity to a focal point of the
orbit. Limiting expressions are obtained that include the asymptotic
probability distribution of rare high-intensity events and a perturbative
formula valid in the limit of weak scarring. For finite system sizes, a single
scaling variable lambda N describes deviations from the semiclassical N ->
infinity limit.
