Structure of three-interval exchange transformations III: Ergodic and spectral properties
Structure of three-interval exchange transformations III: Ergodic and spectral properties
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三区间交换变换的结构 III：遍历和谱特性
DOI：
10.1007/bf02789305
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
L. Zamboni
中科院分区：
文献类型：
--
作者：
S. Ferenczi;Charles Holton;L. Zamboni
本文详细研究了三区间交换变换的谱/遍历性质。我们的方法主要是组合和依赖于丢番图的结果在第一部分和第二部分的组合描述。我们定义了一个递归的方法来生成三个序列的嵌套Rokhlin栈描述系统从测量理论的角度来看，这反过来又给出了一个明确的特征值。我们得到的必要和充分条件弱混合，除了统一所有以前已知的例子，使我们能够展示新的例子弱混合三个区间交流。最后，我们对W. A.具有无理特征值和离散谱的三区间交换的存在性。
In this paper, we present a detailed study of the spectral/ergodic properties of three-interval exchange transformations. Our approach is mostly combinatorial and relies on the diophantine results in Part I and the combinatorial description in Part II. We define a recursive method of generating three sequences of nested Rokhlin stacks which describe the system from a measure-theoretic point of view and which in turn gives an explicit characterization of the eigenvalues. We obtain necessary and sufficient conditions for weak mixing which, in addition to unifying all previously known examples, allow us to exhibit new examples of weakly mixing three-interval exchanges. Finally, we give affirmative answers to two questions posed by W. A. Veech on the existence of three-interval exchanges having irrational eigenvalues and discrete spectrum.