arXiv subjects

Michael Hofbauer-Tsiflakos

Publications and source records attributed to Michael Hofbauer-Tsiflakos.

2 recordsLinked to original sources

arXiv2020

Certain systems of three falling balls satisfy the Chernov-Sinai Ansatz

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.

math.DS↗

arXiv2020

A conditional proof of the non-contraction property for N falling balls

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 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.

math.DS↗