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On cutting sequences of the L-shaped translation surface tiled by three squares

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Abstract

We consider a symbolic coding of bi-infinite non periodic geodesics on the L-shaped translation surface tiled by three squares. Each bi-infinite non periodic geodesic is associated with a cutting sequence corresponding to the sequence of labeled saddle connections hit. We prove that there is a relationship between the cutting sequences and the actions of some affine automorphisms of the translation surface. We also get an explicit formula to determine the direction of a bi-infinite non periodic geodesic by using the corresponding cutting sequence.

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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China

    ShengJian Wu & YuMin Zhong

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  1. ShengJian Wu
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  2. YuMin Zhong
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Correspondence to YuMin Zhong.

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Wu, S., Zhong, Y. On cutting sequences of the L-shaped translation surface tiled by three squares. Sci. China Math. 58, 1311–1326 (2015). https://doi.org/10.1007/s11425-014-4922-z

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  • DOI: https://doi.org/10.1007/s11425-014-4922-z

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