Diagonal changes for surfaces in hyperelliptic components

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• 作者：Vincent Delecroix ; Corinna Ulcigrai
• 关键词：Translation surfaces ; Continued fraction algorithm ; Best approximations ; Flat systoles ; 11J70 ; 37B10 ; 37E35 ; 68R15
• 刊名：Geometriae Dedicata
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：176
• 期：1
• 页码：117-174
• 全文大小：1,962 KB
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• 作者单位：Vincent Delecroix (1)
  Corinna Ulcigrai (2)
  
  1. LaBRI, Universit茅 de Bordeaux, B芒timent A30, 351, cours de la Lib茅ration, 33405聽, Talence cedex, France
  2. School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9168

文摘

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.