论文标题
持续的分数和模块结的量的时期
Periods of continued fractions and volumes of modular knots complements
论文作者
论文摘要
模块化表面上的每个定向的封闭地球都有一个典型的结节，其单位切合束来自地球流动的周期性轨道。我们研究了相关结的量相对于其独特的完整双曲线指标。我们表明，存在封闭的大地测量学序列，该序列根据地球持续分数膨胀的周期而在线性上进行了线性界定。因此，我们为洛伦兹结的某些序列提供了一个体积的上限，以相应的辫子指数线性地进行补充。同样，对于任何刺穿的双曲线表面，我们就某些封闭的大地测量学序列的序列互补的体积限制，就大地测量长度而言。
Every oriented closed geodesic on the modular surface has a canonically associated knot in its unit tangent bundle coming from the periodic orbit of the geodesic flow. We study the volume of the associated knot complement with respect to its unique complete hyperbolic metric. We show that there exist sequences of closed geodesics for which this volume is bounded linearly in terms of the period of the geodesic's continued fraction expansion. Consequently, we give a volume's upper bound for some sequences of Lorenz knots complements, linearly in terms of the corresponding braid index. Also, for any punctured hyperbolic surface we give volume's bounds for the canonical lift complement relative to some sequences of sets of closed geodesics in terms of the geodesics length.
