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

作　　者：WU ShengJian ZHONG YuMin 

机构地区：[1]LMAM and School of Mathematical Sciences, Peking University

出　　处：《Science China Mathematics》2015年第6期1311-1326,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11371035)

摘　　要：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.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.

关 键 词：affine shaped cutting labeled intersection letter infinite compatible saddle explicit 

分 类 号：O186.12[理学—数学]