Rectangle exchange transformations
Rectangle exchange transformations
复制标题
矩形交换变换
DOI：
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发表时间：
1981
期刊：
影响因子：
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通讯作者：
Hans Haller
中科院分区：
文献类型：
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作者：
Hans Haller
我们定义矩形交换变换类似于区间交换变换。区间交换变换是单位区间到自身的映射，通过将区间切割成有限个子区间并重新排列这些子区间而获得。矩形交换变换是单位正方形到自身的映射，通过将正方形切割成有限数量的矩形块并重新排列这些块来获得。本文给出了矩形交换变换的一个极小性条件。我们处理遍历矩形交换变换的各种例子。并对有关问题进行了讨论。
We define rectangle exchange transformations analogously to interval exchange transformations. An interval exchange transformation is a mapping of the unit interval onto itself obtained by cutting the interval up into a finite number of subintervals and rearranging the pieces. A rectangle exchange transformation is a mapping of the unit square onto itself obtained by cutting the square up into a finite number of rectangular pieces and rearranging the pieces. We give a minimality condition for rectangle exchange transformations. We deal with various examples of ergodic rectangle exchange transformations. Related questions are discussed.