𝐶ⁿ interval maps not Borel conjugate to any 𝐶^{∞} map

Ruette, Sylvie

doi:10.1090/S0002-9939-03-07222-8

$C^n$ interval maps not Borel conjugate to any $C^{\infty }$ map
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Proc. Amer. Math. Soc. 132 (2004), 1091-1093 Request permission

Abstract:

We show that there exist interval maps that are not Borel conjugate to any $C^{\infty }$ map. These examples can be chosen to be topologically mixing and $C^n$, for any finite, arbitrarily large $n$.

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