We consider the motion of two point masses along a vertical half-line that are subject to constant gravitational force and collide elastically with each other and the floor. This model was introduced by Wojtkowski who established hyperbolicity and ergodicity in case the lower ball is heavier. Here, we investigate the dynamics in discrete time and prove that, for an open set of the external parameter (the relative mass of the lower ball), the system mixes polynomially-modulo logarithmic factors, correlations decay as O(1/n(2))-and satisfies the Central Limit Theorem.
In this paper we study the system of two falling balls in continuous time. We modell the system by a suspension flow over a two dimensional, hyperbolic base map. By detailed analysis of the geometry of the system we identify special periodic points and show that the ratio of certain periods in continuous time is Diophantine for almost every value of the mass parameter in an interval. Using results of Melbourne ([13]) and our previous achievements [1] we conclude that for these values of the parameter the flow mixes faster than any polynomial. Even though the calculations are presented for the specific physical system, the method is quite general and can be applied to other suspension flows, too.
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