论文标题
洛伦兹吸引子和模块化表面
Lorenz attractors and the modular surface
论文作者
论文摘要
我们定义了在三个球体上定义的几何洛伦兹模型的扩展。该几何模型具有一个不变的一维三叶结结，这是奇点不变的歧管的结合。它类似于在经典参数附近的经典洛伦兹流中产生的不变的三叶结结。我们证明，这种几何模型在拓扑上等同于模块化表面上的测地，一旦压实了后者。
We define an extension of the geometric Lorenz model, defined on the three sphere. This geometric model has an invariant one dimensional trefoil knot, a union of invariant manifolds of the singularities. It is similar to the invariant trefoil knot arising in the classical Lorenz flow near the classical parameters. We prove that this geometric model is topologically equivalent to the geodesic flow on the modular surface, once compactifying the latter.
