A conditional proof of the noncontraction property for N falling balls
Abstract
Wojtkowski's system of $N$, $N \geq 2$, 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 noncontraction 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 DOI:
 10.48550/arXiv.2009.05550
 arXiv:
 arXiv:2009.05550
 Bibcode:
 2020arXiv200905550H
 Keywords:

 Mathematics  Dynamical Systems;
 37D50 (Primary);
 37J10 (Secondary)