PreprintCC BY 4.0arXiv
On disjointness of 3-IETs from mixing and lightly mixing systems
Abstract
In this note we show that all interval exchange transformations of three intervals (3-IETs) are spectrally disjoint from all mixing and disjoint from lightly mixing systems. Until now, it was known that almost every 3-IET is rigid, which implies this property. However, not all 3-IETs are rigid, hence our result is a strict improvement of current knowledge. We then use this result, among many others, to prove that although some 3-IETs are mildly mixing, they are always disjoint in the sense of Furstenberg from lightly mixing systems.
Related
- On disjointness and ℱ-product recurrence with respect to zero entropy systems
- Δ*-Mixing and Products of Full-Scattering Systems
- Statistical properties for irregular observables in slowly mixing hyperbolic systems
- Almost Disjointness Principles and Q-Space Cardinals
- Bernoulli property for skew products of exponentially mixing systems over Anosov bases
BibTeX
@misc{berk2026disjointness,
title = {{On disjointness of 3-IETs from mixing and lightly mixing systems}},
author = {Przemysław Berk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16657},
eprint = {2610.16657},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16657},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On disjointness of 3-IETs from mixing and lightly mixing systems
AU - Przemysław Berk
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16657
UR - https://arxiv.org/abs/2610.16657
AB - In this note we show that all interval exchange transformations of three intervals (3-IETs) are spectrally disjoint from all mixing and disjoint from lightly mixing systems. Until now, it was known that almost every 3-IET is rigid, which implies this property. However, not all 3-IETs are rigid, hence our result is a strict improvement of current knowledge. We then use this result, among many others, to prove that although some 3-IETs are mildly mixing, they are always disjoint in the sense of Furstenberg from lightly mixing systems.
ER -