Nonergodicity and localization of invariant measure for two colliding masses

We show evidence, based on extensive and carefully performed numerical experiments, that the system of two elastic hard-point masses in one dimension is not ergodic for a generic mass ratio and consequently does not follow the principle of energy equipartition. This system is equivalent to a right triangular billiard. Remarkably, following the time-dependent probability distribution in a suitably chosen velocity direction space, we find evidence of exponential localization of invariant measure. For nongeneric mass ratios which correspond to billiard angles which are rational, or weak irrational multiples of π, the system is ergodic, consistent with existing rigorous results.