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

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• 作者：ShengJian Wu ; YuMin Zhong
• 关键词：translation surfaces ; affine automorphisms ; cutting sequences ; 37B10 ; 11J70 ; 37E35
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：58
• 期：6
• 页码：1311-1326
• 全文大小：427 KB
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• 作者单位：ShengJian Wu (1)
  YuMin Zhong (1)
  
  1. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

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.