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arXiv · 1807.09159

On the convergence of renormalizations of piecewise smooth homeomorphisms on the circle

Abdumajid Begmatov·Kleyber Cunha
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Abstract

We study renormalizations of piecewise smooth homeomorphisms on the circle, by considering such maps as generalized interval exchange maps of genus one. Suppose that $Df$ is absolutely continuous on each interval of continuity and $D\ln{Df}\in \mathbb{L}_{p}$ for some $p>1$. We prove, that under certain combinatorial assumptions on $f_{1}$ and $f_{2}$, corresponding renormalizations approach to each other in $C^{1+L_{1}}$-norm.

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Abdumajid Begmatov, Kleyber Cunha. 2018-07-23. On the convergence of renormalizations of piecewise smooth homeomorphisms on the circle. https://arxiv.org/abs/1807.09159

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