New York Journal of Mathematics
Volume 20 (2014) 399-429


Diana Davis

Cutting sequences on translation surfaces

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Published: April 15, 2014
Keywords: Translation surfaces; Veech surfaces; geodesics; symbolic dynamics
Subject: 37E35

We analyze the cutting sequences associated to geodesic flow on a large class of translation surfaces, including Bouw-Möller surfaces. We give a combinatorial rule that relates a cutting sequence corresponding to a given trajectory, to the cutting sequence corresponding to the image of that trajectory under the parabolic element of the Veech group. This extends previous work for regular polygon surfaces to a larger class of translation surfaces. We find that the combinatorial rule is the same as for regular polygon surfaces in about half of the cases, and different in the other half.

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Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2370