Low height geodesics and the Markoff spectrum

Thomas A. Schmidt; Mark Sheingorn

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arXiv · math/0410197

Low height geodesics and the Markoff spectrum

Thomas A. Schmidt·Mark Sheingorn

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Abstract

We classify, in terms of topology of highest arcs, low height non-simple geodesics on the modular hyperbolic punctured sphere with three elliptic fixed points of order two. Of eight possible types, exactly one consists of geodesics that form a bigon about the cusp; we express all such geodesics in terms of Markoff triples. We also show that any geodesic joining two elliptic fixed points has locally isolated height.

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Thomas A. Schmidt, Mark Sheingorn. 2004-10-07. Low height geodesics and the Markoff spectrum. https://arxiv.org/abs/math/0410197

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