One-dimensional motion of inelastic balls. I: Reduction to discrete time (Q1335953)

The authors approximately construct, for some values of system collision constants, an attracting invariant set of Hausdorff dimension greater than one, and an invariant measure on it. The system consists of two balls moving along the interval between walls. The balls and walls are absolutely rigid but inelastic. During the free motion the balls accelerate proportionally to their velocity. The authors consider a Poincaré-type map and prove the kneading, and consequently ergodicity, property.