Rotated Odometers

Henk Bruin; Olga Lukina

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arXiv · 2101.00868

Rotated Odometers

Henk Bruin·Olga Lukina

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Abstract

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

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Henk Bruin, Olga Lukina. 2021-01-04. Rotated Odometers. https://arxiv.org/abs/2101.00868

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