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

Published 17 Dec 2025 in math.DS | (2512.15625v1)

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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