One-dimensional inelastic collapse of four particles: asymmetric collision sequences and spherical billiard reduction

2024/11/15 by Théophile Dolmaire, Dolmaire, Théophile, Eleni Hübner-Rosenau +1
Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2411.10324

openalex publication_date 2024/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient r, and we study the inelastic collapse phenomenon for such a particle system. We study a periodic, asymmetric collision pattern, proving that it can be realized, despite its instability. We prove that we can associate to the four-particle dynamical system another dynamical system of smaller dimension, acting on \1,2,3\ × \mathbbS², and that encodes the collision orders of each trajectory. We provide different representations of this new dynamical system, and study numerically its ω-limit sets. In particular, the numerical simulations suggest that the orbits of such a system might be quasi-periodic.

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