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arXiv · 2512.15625

Existence of a Non-Uniquely Ergodic Interval Exchange Transformation with Flips Possessing Three Invariant Measures

Aleksei Kobzev
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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.

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Aleksei Kobzev. 2025-12-17. Existence of a Non-Uniquely Ergodic Interval Exchange Transformation with Flips Possessing Three Invariant Measures. https://arxiv.org/abs/2512.15625

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