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arXiv · 1310.1052

Diagonal changes for surfaces in hyperelliptic components

Vincent Delecroix·Corinna Ulcigrai
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Abstract

We describe geometric algorithms that generalize the classical continued fraction algorithm for the torus to all translation surfaces in hyperelliptic components of translation surfaces. We show that these algorithms produce all saddle connections which are best approximations in a geometric sense, which generalizes the notion of best approximation for the classical continued fraction. In addition, they allow to list all systoles along a Teichmueller geodesic and all bispecial words which appear in the symbolic coding of linear flows. The elementary moves of the described algorithms provide a geometric invertible extension of the renormalization moves introduced by S. Ferenczi and L. Zamboni for the corresponding interval exchange transformations.

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Vincent Delecroix, Corinna Ulcigrai. 2015-09-10. Diagonal changes for surfaces in hyperelliptic components. https://doi.org/10.1007/s10711-014-9961-7

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