Renormalization for piecewise smooth homeomorphisms on the circle. arXiv:1108.1968
Preprint, arXiv:1108.1968 [math.DS] (2011).
Summary: 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.
MSC:
| 37E10 | Dynamical systems involving maps of the circle |
| 37E05 | Dynamical systems involving maps of the interval |
| 37E20 | Universality and renormalization of dynamical systems |
| 37C05 | Dynamical systems involving smooth mappings and diffeomorphisms |
| 37B10 | Symbolic dynamics |
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