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arXiv · 1207.7299

Cross sections for geodesic flows and α-continued fractions

Pierre Arnoux·Thomas A. Schmidt
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Abstract

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the α-continued fractions, for each $α$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced α-variants.

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Pierre Arnoux, Thomas A. Schmidt. 2012-07-31. Cross sections for geodesic flows and α-continued fractions. https://doi.org/10.1088/0951-7715%2F26%2F3%2F711

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