Ergodicity of hard spheres in a box

We prove that the system of two hard balls in a $\nu$-dimensional ($\nu\ge2$) rectangular box is ergodic and, therefore, actually it is a Bernoulli flow

Conditional Proof of the Ergodic Conjecture for Falling Ball Systems

In this paper we present a conditional proof of Wojtkowski's Ergodicity Conjecture for the system of 1D perfectly elastic balls falling down in a half line under constant gravitational acceleration. Namely, we prove that almost every such system is (completely hyperbolic and) ergodic, by assuming the transversality between different singularities and between singularities and stable (unstable) invariant manifolds.Comment: 9 page