  The system of falling balls is an autonomous Hamiltonian system with a smooth
invariant measure and non-zero Lyapunov exponents almost everywhere. Since
almost three decades, the question of ergodicity is still open. The subject of
this work is to contribute to the solution of the ergodicity conjecture for
three falling balls with a specific mass ratio. The latter is executed in the
following three points: First, we prove the Chernov-Sinai ansatz. Second, we
prove that there is an abundance of least expanding points and, third, we
explain that the proper alignment condition can still be verified and is
actually pointwise equivalent to Chernov's transversality condition. 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.
