Geodesic
Renormalization for piecewise smooth homeomorphisms on the circle
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 441-462
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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.

DOI : 10.1016/j.anihpc.2012.09.004
Classification : 37E10, 37E05, 37E20, 37C05, 37B10
Keywords: Renormalization, Interval exchange transformations, Rauzy–Veech induction, Universality, Homeomorphism on the circle, Convergence 
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     author = {Cunha, Kleyber and Smania, Daniel},
     title = {Renormalization for piecewise smooth homeomorphisms on the circle},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {441--462},
     year = {2013},
     publisher = {Elsevier},
     volume = {30},
     number = {3},
     doi = {10.1016/j.anihpc.2012.09.004},
     zbl = {1338.37052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.09.004/}
}
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Cunha, Kleyber; Smania, Daniel. Renormalization for piecewise smooth homeomorphisms on the circle. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 441-462. doi: 10.1016/j.anihpc.2012.09.004

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