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Certain systems of three falling balls satisfy the Chernov–Sinai ansatz

Volume 250 / 2020

Michael Hofbauer-Tsiflakos Studia Mathematica 250 (2020), 163-192 MSC: Primary 37D50; Secondary 37J10. DOI: 10.4064/sm180519-2-10 Published online: 15 July 2019


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 now, the question of its ergodicity remains open. We contribute to the solution of the ergodicity 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.


  • Michael Hofbauer-TsiflakosFaculty of Mathematics
    University of Vienna
    Oskar-Morgenstern-Platz 1
    1090 Wien, Austria

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