Denjoy’s theorem with exponents

Norton, Alec

doi:10.1090/S0002-9939-99-04852-2

Denjoy’s theorem with exponents
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by Alec Norton PDF

Proc. Amer. Math. Soc. 127 (1999), 3111-3118 Request permission

Abstract:

If $X$ is the (unique) minimal set for a $C^{1+\alpha }$ diffeomorphism of the circle without periodic orbits, $0<\alpha <1$, then the upper box dimension of $X$ is at least $\alpha$. The method of proof is to introduce the exponent $\alpha$ into the proof of Denjoy’s theorem.

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