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

2025/12/17 by Kobzev, Aleksei
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.15625

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.

Citations

• Triangle tiling billiards and the exceptional family of their escaping trajectories: circumcenters and Rauzy gasket

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