论文标题
有效的刚性远离边界的中央对称台球
Effective rigidity away from the boundary for centrally-symmetric billiards
论文作者
论文摘要
在本文中，我们研究了中央对称的Birkhoff台球表。我们引入了一个封闭的不变套件$ \ MATHCAL {M} _ \ MATHCAL {B} $，由位于区域内的台球地图的本地轨道组成，位于区域内$ \ Mathcal {B} $由两个不变曲线界限为$ 4 $ periodic Orbits。我们从上面的有效界限就曲线的等速缺陷的量度衡量。且仅当曲线为圆时，就会发生平等情况。
In this paper we study centrally symmetric Birkhoff billiard tables. We introduce a closed invariant set $\mathcal{M}_\mathcal{B}$ consisting of locally maximizing orbits of the billiard map lying inside the region $\mathcal{B}$ bounded by two invariant curves of $4$-periodic orbits. We give an effective bound from above on the measure of this invariant set in terms of the isoperimetric defect of the curve. The equality case occurs if and only if the curve is a circle.
