Examples of exponentially many collisions in a hard ball system

Abstract

Consider the system of $n$ identical hard balls in ${\mathbb{R}}^3$ moving freely and colliding elastically. We show that there exist initial conditions such that the number of collisions is exponential in $n$.

v2: more detailed proof of Lemma 2.2, some misprints corrected. To appear in Ergodic Theory & Dynamical Systems

References in corpus (2)

• A lower bound for the number of elastic collisions
• Estimating the number and the strength of collisions in molecular dynamics

Cited by in corpus (4)

• A splash in a one-dimensional cold gas
• Hard spheres dynamics: weak vs hard collisions
• Estimating the number and the strength of collisions in molecular dynamics
• An improved upper bound on the number of billiard ball collisions