Proof of Wojtkowski's Falling Particle Conjecture

TL;DR

This paper provides an unconditional proof that almost all one-dimensional falling elastic particle systems under gravity are ergodic and hyperbolic, confirming Wojtkowski's conjecture using a new algebraic method.

Contribution

It introduces a novel algebraic approach to prove Wojtkowski's ergodicity conjecture for almost every 1D falling particle system.

Findings

Almost every 1D falling elastic particle system is ergodic.

The systems are proven to be completely hyperbolic.

The proof is unconditional and applies to almost all such systems.

Abstract

In this paper we present an unconditional proof of Wojtkowski's Ergodicity Conjecture for almost every system of 1D perfectly elastic balls falling down in a half line under constant gravitational acceleration. Namely, by introducing a new algebraic approach, we prove that almost every such system is (completely hyperbolic and) ergodic.