Typical Weak Mixing and Exceptional Spectral Properties for Interval Translation Mappings
Dynamical Systems
2026-03-23 v1
Abstract
We investigate weak mixing for some classes of interval translation mappings. We give two distinct proofs that a typical Bruin-Troubetzkoy interval translation mapping is weakly mixing. Moreover, we show that the second approach extends to other classes of interval translation mappings. In particular, we show that Bruin interval translation mappings on any number of intervals are typically weak mixing. Finally, we construct the first examples of non weak mixing Bruin-Troubetzkoy ITM of infinite type.
Keywords
Cite
@article{arxiv.2603.19401,
title = {Typical Weak Mixing and Exceptional Spectral Properties for Interval Translation Mappings},
author = {Mauro Artigiani and Artur Avila and Sébastien Ferenczi and Pascal Hubert and Alexandra Skripchenko},
journal= {arXiv preprint arXiv:2603.19401},
year = {2026}
}
Comments
34 pages, 9 figures. Comments are welcome!