JournalsaihpcVol. 30, No. 3pp. 441–462

Renormalization for piecewise smooth homeomorphisms on the circle

  • Kleyber Cunha

    Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, CEP 40170-110, Salvador, BA, Brazil

  • Daniel Smania

    Departamento de Matemática, ICMC/USP-Campus de São Carlos, Caixa Postal 668, CEP 13560-970, São Carlos, SP, Brazil
Renormalization for piecewise smooth homeomorphisms on the circle cover
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Abstract

In this work we study the renormalization operator acting on piecewise smooth homeomorphisms on the circle, that turns out to be essentially the study of Rauzy–Veech renormalizations of generalized interval exchange maps with genus one. In particular we show that renormalizations of such maps with zero mean nonlinearity and satisfying certain smoothness and combinatorial assumptions converge to the set of piecewise affine interval exchange maps.

Cite this article

Kleyber Cunha, Daniel Smania, Renormalization for piecewise smooth homeomorphisms on the circle. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 3, pp. 441–462

DOI 10.1016/J.ANIHPC.2012.09.004