Habibulla Akhadkulov, and Mohd. Salmi Md. Noorani, and Sokhobiddin Akhatkulov, (2014) Notes on conjugacies and renormalisations of circle diffeomorphisms with breaks. Journal of Quality Measurement and Analysis, 10 (2). pp. 8798. ISSN 18235670

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Abstract
Let f be an orientationpreserving circle diffeomorphism with irrational “rotation number” of bounded type and finite number of break points, that is, the derivative f ′ has discontinuities of first kind at these points. Suppose f ′ satisfies a certain Zygmund condition which be dependent on parameter γ > 0 on each continuity intervals. We prove that the RauzyVeech renormalisations of f are approximated by Mobius transformations in C1 norm if γ ∈(0,1] and in C2 norm if γ ∈(1,∞) . In particular, we show that if f has zero mean nonlinearity, renormalisation of such maps approximated by piecewise affine interval exchange maps. Further, we consider two circle homeomorphisms with the same irrational “rotation number” of bounded type and finite number of break points. We prove that if they are not break equivalent then the conjugating map between these two maps is singular.
Item Type:  Article 

Keywords:  conjugacy; circle diffeomorphism; break point; renormalisation; interval exchange transformation; Mobius transformation; RauzyVeech induction 
Journal:  Journal of Quality Measurement and Analysis 
ID Code:  8610 
Deposited By:  ms aida  
Deposited On:  14 May 2015 07:47 
Last Modified:  14 Dec 2016 06:47 
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