Trajectories of rotations
Trajectories of rotations
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旋转轨迹
DOI：
10.4064/aa-87-3-209-217
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发表时间：
1999
期刊：
影响因子：
0.7
通讯作者：
P. Hubert
中科院分区：
文献类型：
--
作者：
P. Arnoux;S. Ferenczi;P. Hubert
= 0;对于其他点，虽然该方法在原理上是容易的，但必须克服技术性问题以得到可管理的公式。[ITO-YAS]中给出了一个算法，[RAU 1]、[RAU 2]中也给出了另一个算法，但它们都没有使用标准的连分式逼近。在[SID-VER]中详细研究了一个密切相关的过程，使用adicsystems的概念;在该文件中显示了两种不同的近似，彼此对偶;我们将在本文的最后从符号动力学的角度回到这个话题。[ARN-FIS]给出了这个问题的一般概述，涉及符号动力学，算术和一些几何模型。所有这些方法都使用了动力学的概念，归纳，这成为著名的劳齐归纳（[RAU 3]）。另一种技术，使用形式幂级数，被用于[NIS-SHI-TAM];这篇论文后来被Komatsu纠正，他的论文（[KOM 1]-[KOM 5]）给出了这些序列唯一已知的完整特征，它与规范连分式逼近有关。下面的结构给出了Sturmian序列的概念特征
= 0; for other points, although the method is easy in principle,technicalities have to be overcome to get manageable formulas. An algorithmis given in [ITO-YAS] and another can be deduced from [RAU1], [RAU2],but they do not use the standard continued fraction approximation. A closelyrelated process is studied in detail in [SID-VER], using the notion of adicsystems; in that paper two different kinds of approximation are shown, dualto each other; we shall come back to this topic from the point of viewof symbolic dynamics at the end of the present paper. [ARN-FIS] gives ageneral overview of the subject, relating symbolic dynamics, arithmetic andsome geometric models. All these approaches use the dynamical notion ofinduction, which became famous as the Rauzy induction ([RAU3]). Anothertechnique, using formal power series, was used in [NIS-SHI-TAM]; this paperwas later corrected by Komatsu, and his papers ([KOM1]–[KOM5]) give theonly known complete characterization of these sequences which is linked tothe canonical continued fraction approximation.The following construction gives a conceptual characterization of theSturmian sequence