Existence of a Non-Uniquely Ergodic Interval Exchange Transformation with Flips Possessing Three Invariant Measures
Dynamical Systems
2026-05-20 v4
Abstract
We present the first explicit example of an interval exchange transformation with flips (FIET) possessing three distinct invariant ergodic measures. The proof is based on a generalization of M. Keane's method, using the Rauzy induction adapted for FIETs, which contributes to the study of the ergodic properties of this class of dynamical systems.
Keywords
Cite
@article{arxiv.2512.15625,
title = {Existence of a Non-Uniquely Ergodic Interval Exchange Transformation with Flips Possessing Three Invariant Measures},
author = {Aleksei Kobzev},
journal= {arXiv preprint arXiv:2512.15625},
year = {2026}
}