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We prove that two C
3 critical circle maps with the same rotation number in a special set ? are C
1+α conjugate for some α>0 provided their successive renormalizations converge together at an exponential rate in the C
0 sense. The set ? has full Lebesgue measure and contains all rotation numbers...
We study solutions of first order partial differential relations Du∈K, where u:Ω⊂ℝ
is a Lipschitz map and K is a bounded set in m×n matrices, and extend Gromov’s theory of convex integration in two ways. First, we allow for additional constraints on the minors of Du and second we replace...
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