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affine dynamics 1C1 regularity 1circle diffeomorphisms 1denjoy counterexample 1invariant Cantor set 1rotation number 1

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math.DS2026

Denjoy examples of class with affine dynamics outside the invariant Cantor set

Victor Kleptsyn, Andrés Navas

The authors construct, for any irrational rotation number, a C¹ circle diffeomorphism (a Denjoy example) that is exactly affine on each interval of the complement of its invariant…