论文标题
三个掉落球的某些系统满足Chernov-Sinai Ansatz
Certain systems of three falling balls satisfy the Chernov-Sinai Ansatz
论文作者
论文摘要
掉落球的系统是一种自主的汉密尔顿系统，几乎到处都有一个平稳的不变度和非零的Lyapunov指数。在近三十年的新事物中，其终结性问题仍然开放。我们有助于求解生物瘤性猜想的三个掉落球，在以下两个点中具有特定的质量比：首先，我们证明了Chernov-Sinai Ansatz。其次，我们证明有足够的扩展点。对于上述特定的质量比，可以将配置空间展开至台球表，这是特别感兴趣的。
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.
