Interval exchange transformation

Graph of interval exchange transformation (in black) with and . In blue, the orbit generated starting from .

In mathematics, an interval exchange transformation[1] 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. They arise naturally in the study of polygonal billiards and in area-preserving flows.

  1. ^ Keane, Michael (1975), "Interval exchange transformations", Mathematische Zeitschrift, 141: 25–31, doi:10.1007/BF01236981, MR 0357739.