论文标题
$ psl（2，\ mathbb {z}）\ backslash \ mathbb {h} $和stern-brocot树的圆锥流的庞加莱地图
A Poincaré map for the horocycle flow on $PSL(2,\mathbb{Z})\backslash \mathbb{H}$ and the Stern-Brocot tree
论文作者
论文摘要
我们为模块化表面$ psl（2，\ mathbb {z}）\ backslash \ backslash \ mathbb {h h} $构造了poincaré映射$ \ mathcal {p} _h $，用于模块化表面$ psl（2，\ mathbb {z}）上的正性烟节流。特别是，我们对$ \ Mathcal {p} _h $的周期性轨道进行了完整的表征，并证明它们相对于$ \ Mathcal {p} _H $的不变度度量进行了等分，并且可以通过使用有理数的胸骨树木树在树上进行组织。此外，我们还引入了$ \ Mathcal {p} _h $的时间重新分配化，该化可以深入了解非周期轨道的动力学。本文构成了通过纯动力学方法研究肉鸡流动的动力学特性的第一步。
We construct a Poincaré map $\mathcal{P}_h$ for the positive horocycle flow on the modular surface $PSL(2,\mathbb{Z})\backslash \mathbb{H}$, and begin a systematic study of its dynamical properties. In particular we give a complete characterisation of the periodic orbits of $\mathcal{P}_h$, and show that they are equidistributed with respect to the invariant measure of $\mathcal{P}_h$ and that they can be organised in a tree by using the Stern-Brocot tree of rational numbers. In addition we introduce a time-reparameterisation of $\mathcal{P}_h$ which gives an insight into the dynamics of the non-periodic orbits. This paper constitutes a first step in the study of the dynamical properties of the horocycle flow by purely dynamical methods.
