Skew-product systems over infinite interval exchange transformations

Abstract We study the ergodic properties (recurrence, discrepancy, diffusion coefficients and ergodicity itself) of a class of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> </mml:mrow> </mml:math> -extensions over infinite interval exchange transformations called rotated odometers. The choice of a skew-function is motivated by the use in the study of parallel flows on a particular staircase manifold of infinite genus.