Rotated odometers

We describe the infinite interval exchange transformations, called rotated odometers, which are obtained as compositions of finite transformations and von Neumann–Kakutani map. show that with respect to Lebesgue measure on unit interval, every such transformation is measurably isomorphic first return map a rational parallel flow translation surface area genus number ends. dynamics odometers by means Bratteli–Vershik systems, derive several their topological ergodic properties, investigate in detail range specific examples odometers.