Interval exchange transformation

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.

Let ${\displaystyle n>0}$ and let ${\displaystyle \pi }$ be a permutation on ${\displaystyle 1,\dots ,n}$. Consider a vector ${\displaystyle \lambda =(\lambda _{1},\dots ,\lambda _{n})}$ of positive real numbers (the widths of the subintervals), satisfying

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