Coding of a translation of the two-dimensional torus
Coding of a translation of the two-dimensional torus
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二维环面平移的编码
DOI：
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发表时间：
2009
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通讯作者：
N. Chevallier
中科院分区：
文献类型：
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作者：
N. Chevallier
设α在二维环T2=1R2/Z2中。假设平移映射T：x→x x+α遍历。我们给出了映射T的符号编码，它与一维平移的Sturmian编码有几个共同的性质。符号动力系统与几何动力系统(T2，T)度量同构。该编码具有二次增长的复杂性和2-平衡。此外，存在几何支撑，编码与Z2在R2上的作用的基本区域有关，也与有界余数集有关。
Let α be in the two-dimensional torus T2 = R2/Z2. Assume that the translation map T : x → x + α acts ergodically. We present a symbolic coding of the map T which shares several properties with the Sturmian coding of a one-dimensional translation. The symbolic dynamical system is metrically isomorphic to the geometric dynamical system (T2, T). The coding is of quadratic growth complexity and 2-balanced. Moreover, there is a geometric underpinning, the coding is related to a fundamental domain for the action of Z2 on R2 and also to bounded remainder sets.