Renormalization for piecewise smooth homeomorphisms on the circle
Kleyber CunhaDepartamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, CEP 40170-110, Salvador, BA, BrazilDaniel SmaniaDepartamento de Matemática, ICMC/USP-Campus de São Carlos, Caixa Postal 668, CEP 13560-970, São Carlos, SP, Brazil
2012en
ABI
Annotatsiya
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.
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