Tom Schmidt – Geodesic flow and natural extensions for continued fractions

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Date(s) - 5 juillet 2013

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Arnoux used Teichmueller flow to show that regular continued fractions arise as a factor of a cross section for the geodesic flow on the modular surface. Luzzi and Marmi asked if also the alpha-continued fractions of Nakada can arise as a factor of a cross section. With Arnoux, extending work with Kraaikamp and Steiner, we showed that this is so. Using these cross sections, with Fisher we gave a version of Moeckel’s result on the distribution of the numerators and denominators of the convergents arising from such continued fraction expansions. The talk will start with the basics, and include quite a few figures.