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arXiv · 1906.07250

On Cross Sections to the Geodesic and Horocycle Flows on Quotients of $\operatorname{SL}(2, \mathbb{R})$ by Hecke Triangle Groups $G_q$

Diaaeldin Taha
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Abstract

In this paper, we provide a model for cross sections to the geodesic and horocycle flows on $\operatorname{SL}(2, \mathbb{R})/G_q$ using an extension of a heuristic of P. Arnoux and A. Nogueira. Our starting point is a continued fraction algorithm related to the group $G_q$, and a cross section to the horocycle flow on $\operatorname{SL}(2, \mathbb{R})/G_q$ from a previous paper. As an application, we get the natural extension and invariant measure for a symmetric $G_q$-Farey interval map resulting from projectivizing the aforementioned continued fraction algorithm.

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Diaaeldin Taha. 2019-06-17. On Cross Sections to the Geodesic and Horocycle Flows on Quotients of $\operatorname{SL}(2, \mathbb{R})$ by Hecke Triangle Groups $G_q$. https://arxiv.org/abs/1906.07250

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