论文标题
n落球的非征收特性的有条件证明
A conditional proof of the non-contraction property for N falling balls
论文作者
论文摘要
Wojtkowski的$ n $，$ n \ geq 2 $，掉落球是一种具有奇异性的非均匀双曲光滑动力学系统。这个系统是否是千古的仍然是一个悬而未决的问题。我们通过证明非征收特性，以严格的无限制为条件，为肯定的答案做出了贡献。对于一定的质量比，可以将配置空间展开到满足艰巨的适当比对条件的台球表。我们证明，上述三个自由度的展开系统是奇异的。
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.
