Certain systems of three falling balls satisfy the Chernov–Sinai ansatz
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Publication:5207344
DOI10.4064/SM180519-2-10zbMATH Open1437.37029arXiv2009.05543OpenAlexW2957872440WikidataQ127484609 ScholiaQ127484609MaRDI QIDQ5207344
Author name not available (Why is that?)
Publication date: 19 December 2019
Published in: (Search for Journal in Brave)
Abstract: The system of falling balls is an autonomous Hamiltonian system with a smooth invariant measure and non-zero Lyapunov exponents almost everywhere. For almost three decades new, the question of its ergodicity remains open. We contribute to the solution of the erogodicity conjecture for three falling balls with a specific mass ratio in the following two points: First, we prove the Chernov-Sinai ansatz. Second, we prove that there is an abundance of sufficiently expanding points. It is of special interest that for the aforementioned specific mass ratio, the configuration space can be unfolded to a billiard table, where the proper alignment condition holds.
Full work available at URL: https://arxiv.org/abs/2009.05543
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