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arXiv · 2001.10989

Minimal non uniquely ergodic flipped IETs

A. Linero Bas·G. Soler López
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Abstract

In this paper we prove the existence of minimal non uniquely ergodic flipped IETs. In particular, we build explicitly minimal non uniquely ergodic $(10,k)$-IETs for any $1\leq k \leq 10$. This answers an open question posed in [C.~Gutierrez, S.~Lloyd, V.~Medvedev, B.~Pires, and E.~Zhuzhoma.Transitive circle exchange transformations with flips. Discrete Contin. Dyn. Syst.,26 (1):251--263, 2010]. As a consequence, we also derive the existence of transitive non uniquely ergodic $(n,k)$-IETs, for any $n\geq 10$ and $1\leq k\leq n$ if $n$ is even, and $1\leq k\leq n-1$ if $n$ is odd.

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A. Linero Bas, G. Soler López. 2020-01-29. Minimal non uniquely ergodic flipped IETs. https://arxiv.org/abs/2001.10989

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