Abstract
In this paper we build the renormalization horseshoe for the circle homeomorphisms, which are C 2+α-smooth everywhere except for one point, and at that point have a jump in first derivative. We also show that two such homeomorphisms are C 1-smoothly conjugate for a certain class of rotation numbers, which include non-Diophantine numbers with arbitrarily high rate of growth.
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Communicated by G. Gallavotti
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Khanin, K., Teplinsky, A. Renormalization Horseshoe and Rigidity for Circle Diffeomorphisms with Breaks. Commun. Math. Phys. 320, 347–377 (2013). https://doi.org/10.1007/s00220-013-1706-1
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DOI: https://doi.org/10.1007/s00220-013-1706-1