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

2018/07/23 by Begmatov, Abdumajid, Cunha, Kleyber
#37B10 #37C05 #37E05 #37E10 #37E20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.09159

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 DlnDf∈ \mathbbL_p for some p>1. We prove, that under certain combinatorial assumptions on f₁ and f₂, corresponding renormalizations approach to each other in C^1+L₁-norm.

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