论文标题
弱混合多边形台球
Weakly Mixing Polygonal Billiards
论文作者
论文摘要
我们证明存在一组残留的（非理性）多边形，例如相对于liouville措施（在单位切线束上），台球流量很弱。这是通过Baire类别参数的，从表明对于任何翻译表面，几乎每对方向的流量都相对于Lebesgue度量而言是奇异的。反过来，这是通过证明在每个翻译表面的表面，几乎每对方向的流动都不共享非平凡的共同特征值。
We prove that there exists a residual set of (non-rational) polygons such the billiard flow is weakly mixing with respect to the Liouville measure (on the unit tangent bundle to the billiard). This follows, via a Baire category argument, from showing that for any translation surface the product of the flows in almost every pair of directions is ergodic with respect to Lebesgue measure. This in turn is proven by showing that for every translation surface the flows in almost every pair of directions do not share non-trivial common eigenvalues.
