# Linearization of generalized interval exchange maps

@article{Marmi2010LinearizationOG,
title={Linearization of generalized interval exchange maps},
author={Stefano Marmi and Pierre Moussa and J. C. Yoccoz},
journal={arXiv: Dynamical Systems},
year={2010}
}
• Published 5 March 2010
• Mathematics
• arXiv: Dynamical Systems
A standard interval exchange map is a one-to-one map of the interval which is locally a translation except at finitely many singularities. We define for such maps, in terms of the Rauzy-Veech continuous fraction algorithm, a diophantine arithmetical condition called restricted Roth type which is almost surely satisfied in parameter space. Let $T_0$ be a standard interval exchange map of restricted Roth type, and let $r$ be an integer $\geq 2$. We prove that, amongst $C^{r+3}$ deformations of…
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Let T be a 2-dimensional torus equipped with a flat Riemannian metric and a vector field which is unitary and parallel for that metric. Then there exists a unique lattice Λ ⊂ R such that T is
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