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arXiv · 2411.06419

On the uniqueness of affine IETs semi-conjugated to IETs

Frank Trujillo
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Abstract

We prove that for almost every irreducible interval exchange transformation $T$ and for any vector $\omega$ in its associated central-stable space (with respect to the Kontsevich-Zorich cocycle) there exists a unique AIET, up to normalization of its domain, semi-conjugated to $T$ and whose log-slope vector equals $\omega$. This provides a partial answer to a question raised by S. Marmi, P. Moussa, and J.-C. Yoccoz.

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Frank Trujillo. 2024-11-10. On the uniqueness of affine IETs semi-conjugated to IETs. https://arxiv.org/abs/2411.06419

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