2020/09/11 by Michael Hofbauer-Tsiflakos, Hofbauer-Tsiflakos, Michael
Mathematics · Physics and Astronomy · #37D50 (Primary) #37J10 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2009.05550
openalex publication_date 2020/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Wojtkowski's system of N, N ≥ 2, falling balls is a nonuniformly hyperbolic smooth dynamical system with singularities. It is still an open question whether this system is ergodic. We contribute towards an affirmative answer, by proving the non-contraction property, conditioned by the assumption of strict unboundedness. For a certain mass ratio the configuration space can be unfolded to a billiard table where the daunting proper alignment condition is satisfied. We prove, that the aforementioned unfolded system with three degrees of freedom is ergodic.