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arXiv · 1703.09002

On certain orbits of geodesic flow and (a,b)-continued fractions

Manoj Choudhuri
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Abstract

In this article, we characterize two kinds of exceptional orbits of the geodesic flow associated with the Modular surface in terms of a two-parameter family of continued fraction expansion of endpoints of the lifts to the hyperbolic plane of the corresponding geodesics. As a consequence, we obtain an extension of Dani correspondence between homogeneous dynamics and Diophantine approximation.

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Manoj Choudhuri. 2020-06-09. On certain orbits of geodesic flow and (a,b)-continued fractions. https://arxiv.org/abs/1703.09002

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