First explicit non-uniquely ergodic FIET with three invariant ergodic measures, obtained by generalizing Keane's construction via Rauzy induction adapted to flips.
Nogueira Almost all interval exchange transformations with flips are nonergodic Ergodic Theory and Dynamical Systems 9 (1989)
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Existence of a Non-Uniquely Ergodic Interval Exchange Transformation with Flips Possessing Three Invariant Measures
First explicit non-uniquely ergodic FIET with three invariant ergodic measures, obtained by generalizing Keane's construction via Rauzy induction adapted to flips.