English

Conditional Proof of the Ergodic Conjecture for Falling Ball Systems

Dynamical Systems 2022-11-22 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2211.10874,
  title  = {Conditional Proof of the Ergodic Conjecture for Falling Ball Systems},
  author = {Nandor Simanyi},
  journal= {arXiv preprint arXiv:2211.10874},
  year   = {2022}
}

Comments

9 pages

R2 v1 2026-06-28T06:17:45.665Z