论文标题
曾经被刺激的圆环上的地震
Earthquakes on the once-punctured torus
论文作者
论文摘要
我们研究了与曾经启动的圆环的简单闭合曲线相关的Teichmüller空间上的地震变形。我们描述了两种方法，以获得任何简单的封闭曲线的明确形式的地震变形。第一种方法植根于线性复发关系，第二种方法是双曲几何形状中的第二种方法。这两种方法对齐，提供了地震变形的代数和几何解释。我们将表达式转换为Teichmüller空间的其他坐标系，以进一步检查地震变形。两个曲线家族用作例子。检查每种行为的限制行为，可以洞悉有关测量的测量层压的地震，其中简单的封闭曲线是一种特殊情况。
We study earthquake deformations on Teichmüller space associated with simple closed curves of the once-punctured torus. We describe two methods to get an explicit form of the earthquake deformation for any simple closed curve. The first method is rooted in linear recurrence relations, the second in hyperbolic geometry. The two methods align, providing both an algebraic and geometric interpretation of the earthquake deformations. We convert the expressions to other coordinate systems for Teichmüller space to examine earthquake deformations further. Two families of curves are used as examples. Examining the limiting behaviour of each gives insight into earthquakes about measured geodesic laminations, of which simple closed curves are a special case.
