On the ergodicity of infinite antisymmetric extensions of symmetric IETs

Przemysław Berk; Frank Trujillo

doi:10.4171/jems/1635

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On the ergodicity of infinite antisymmetric extensions of symmetric IETs

Przemysław Berk
Nicolaus Copernicus University, Torun, Poland
Frank Trujillo
Universität Zürich, Zürich, Switzerland; Centre de Recerca Matemàtica, Bellaterra, Spain

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Abstract

We consider skew product extensions over symmetric interval exchange transformations on the unit interval $[0, 1)$ with respect to the cocycle $f = χ_{(0, 1/2)} - χ_{(1/2, 1)}$ . We prove that for almost every interval exchange transformation $T$ with symmetric combinatorial data, the skew product $T_{f} : [0, 1) \times Z \to [0, 1) \times Z$ given by $T_{f} (x, r) = (T (x), r + f (x))$ is ergodic with respect to the product of the Lebesgue and counting measures.

Cite this article

Przemysław Berk, Frank Trujillo, On the ergodicity of infinite antisymmetric extensions of symmetric IETs. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1635