论文标题
地球流量和所有持续分数的母亲
Geodesic flows and the mother of all continued fractions
论文作者
论文摘要
我们在模块表面$ \ MATHCAL {m} = \ perperatorName {psl}（2，\ Mathbb {z}）\ Backslash \ Mathbb {h} $，切割序列，切割序列，并定期使用缓慢收敛的Lehner和Farey Flations $（1）$（1）$（1）$（1）雷纳继续分数。我们还引入了一种替代插入和奇异算法，用于Farey扩展和其他非隔离的持续分数，以及对Farey扩展的替代双重扩展，以便在自然扩展图下，$ \ frac {dxdy} {（1+xy）^2} $是无机的。
We extend the Series' connection between the modular surface $\mathcal{M}=\operatorname{PSL}(2,\mathbb{Z})\backslash\mathbb{H}$, cutting sequences, and regular continued fractions to the slow converging Lehner and Farey continued fractions with digits $(1,+1)$ and $(2,-1)$ in the notation used for the Lehner continued fractions. We also introduce an alternative insertion and singularization algorithm for Farey expansions and other non-semiregular continued fractions, and an alternative dual expansion to the Farey expansions so that $\frac{dxdy}{(1+xy)^2}$ is invariant under the natural extension map.
