Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the renormalizations of circle homeomorphisms with several break
  points   Let $f$ be an orientation preserving homeomorphisms on the circle with
several break points, that is, its derivative $Df$ has jump discontinuities at
these points. We study Rauzy-Veech renormalizations of piecewise smooth circle
homeomorphisms, by considering such maps as generalized interval exchange maps
with genus one. Suppose that $Df$ is absolutely continuous on the each interval
of continuity and $D\ln{Df}\in \mathbb{L}_{p}$ for some $p>1$. We prove that,
under certain combinatorial assumptions on $f$, renormalizations $R^{n}(f)$ are
approximated by piecewise M\"{o}bus functions in $C^{1+L_{1}}$-norm, that
means, $R^{n}(f)$ are approximated in $C^{1}$-norm and $D^{2}R^{n}(f)$ are
approximated in $L_{1}$-norm. In particular, if $f$ has trivial product of size
of breaks, then the renormalizations are approximated by piecewise affine
interval exchange maps.

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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con