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

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.

13 pages. arXiv admin note: substantial text overlap with arXiv:1706.03654

Cited by in corpus (1)

• On the renormalizations of circle homeomorphisms with several break points