平面开台球中非徘徊集的豪斯多夫维数的可微性
Differentiability of Hausdorff dimension of the non-wandering set in a planar open billiard
摘要：
我们考虑满足无食条件的平面上的开台球。我们表明，在非徘徊集的点取决于微分变形的边界的台球。利用Bowen方程估计了台球非徘徊集的豪斯多夫维数。最后，我们表明，豪斯多夫维数取决于微分足够光滑的变形边界的台球，并估计相对于这种变形的衍生物。
英文摘要：
We consider open billiards in the plane satisfying the no-eclipse condition. We show that the points in the non-wandering set depend differentiably on deformations to the boundary of the billiard. We use Bowen's equation to estimate the Hausdorff dimension of the non-wandering set of the billiard. Finally we show that the Hausdorff dimension depends differentiably on sufficiently smooth deformations to the boundary of the billiard, and estimate the derivative with respect to such deformations.
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