On multiple recurrence and other properties of “nice” infinite measure preserving transformations
On multiple recurrence and other properties of “nice” infinite measure preserving transformations
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关于“好”无限测度保留变换的多重递归和其他属性
DOI：
10.1017/etds.2015.89
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发表时间：
2016
影响因子：
0.9
通讯作者：
H. Nakada
中科院分区：
文献类型：
--
作者：
J. Aaronson;H. Nakada
我们研究了圆的分段旋转与区间交换映射之间的某种对偶关系。2005年，Cruz和da-Rocha[推广了Gauss映射和一些关于连分式的经典定理。非线性18(2005)，505-525]引入了一个由圆的分段旋转产生的‘城堡’的概念。我们推广了他们的想法，引入了城堡的一个连续版本，我们证明了它等价于Veech的拉链矩形[区间交换映射空间上的变换的高斯度量]。安。数学的一部分。(2)115(1982)、201-242]。我们证明了定义在城堡上的相当自然的映射表示Rauzy映射的自然扩张的逆。
We investigate a certain dual relationship between piecewise rotations of a circle and interval exchange maps. In 2005, Cruz and da Rocha [A generalization of the Gauss map and some classical theorems on continued fractions. Nonlinearity18 (2005), 505–525] introduced a notion of ‘castles’ arising from piecewise rotations of a circle. We extend their idea and introduce a continuum version of castles, which we show to be equivalent to Veech’s zippered rectangles [Gauss measures for transformations on the space of interval exchange maps. Ann. of Math. (2) 115 (1982), 201–242]. We show that a fairly natural map defined on castles represents the inverse of the natural extension of the Rauzy map.