We study a family of infinite interval exchange transformations on the unit interval emerging from compositions of the Von Neumann-Kakutani map (dyadic odometer) with rational rotations (or more generally permutations of equal-length intervals. Hence the name ``rotated odometers’’. By means of renormalization (similar to Rauzy-Veech induction) we cam translate the problem into one on symbolic substitutions, and determine the dynamic and ergodic structure of these rotated odometers.

This is joint work with Olga Lukina