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In mathematics, an interval exchange transformation〔.〕 is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit interval, and the transformation acts by cutting the interval into several subintervals, and then permuting these subintervals. ==Formal definition== Let and let be a permutation on . Consider a vector of positive real numbers (the widths of the subintervals), satisfying : Define a map called the interval exchange transformation associated to the pair as follows. For let : Then for , define : if lies in the subinterval . Thus acts on each subinterval of the form by a translation, and it rearranges these subintervals so that the subinterval at position is moved to position . 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Interval exchange transformation」の詳細全文を読む スポンサード リンク
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