Renormalization for piecewise smooth homeomorphisms on the circle

Details Renormalization for piecewise smooth homeomorphisms on the circle Renormalization for piecewise smooth homeomorphisms on the circle

2011-08-09

arxiv.org/abs/1108.1968v1

Mathematics

Dynamical Systems

30 pages

Scientific paper

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 exchanges maps with genus one. In particular we show that renormalizations of such maps with zero mean nonlinearity and satisfying certain smoothness and combinatorial assumptions converges to the set of piecewise affine interval exchange maps.

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