Robust rigidity for circle diffeomorphisms with singularities |
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| Authors: | K. Khanin A. Teplinsky |
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| Affiliation: | (1) Department of Mathematics, University of Toronto, 40 St. George St., Toronto, M5S 2E4, Ontario, Canada;(2) Landau Institute of Theoretical Physics, Russian Academy of Sciences, Moscow, 117 940, Russia;(3) Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska Street, 01601 Kiev, Ukraine |
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| Abstract: | We prove that under certain regularity conditions imposed on the renormalizations of two circle diffeomorphisms with singularities, their C 1-smooth equivalence follows from exponential convergence of those renormalizations. As an easy corollary, any two analytical critical circle maps with the same order of critical points and the same irrational rotation number are C 1-smoothly conjugate. |
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