论文标题
分散台球系统的频谱刚度
On Length Spectrum Rigidity of Dispersing Billiard Systems
论文作者
论文摘要
我们考虑通过删除满足非复制条件的三个凸的分析散射器而形成的平面中分散台球系统的类别。该系统中的碰撞图被偶联到一个子移位，提供了周期点的自然标记。我们研究此类系统的明显长度频谱刚度的问题。我们表明，当且仅当它们的碰撞图在分析上互相共轭附近，并且两个散射器和标记的长度光谱共同确定第三个散射器时，我们才显示两个这样的系统具有相同的标记长度频谱。
We consider the class of dispersing billiard systems in the plane formed by removing three convex analytic scatterers satisfying the non-eclipse condition. The collision map in this system is conjugated to a subshift, providing a natural labeling of periodic points. We study the problem of marked length spectrum rigidity for this class of systems. We show that two such systems have the same marked length spectrum if and only if their collision maps are analytically conjugate to each other near a homoclinic orbit and that two scatterers and the marked length spectrum together uniquely determine the third scatterer.
