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Published online by Cambridge University Press: 07 September 2017
We prove that, for almost all irrational
$\unicode[STIX]{x1D70C}\in (0,1)$
, the Hausdorff dimension of the invariant measure of a
$C^{2+\unicode[STIX]{x1D6FC}}$
-smooth
$(\unicode[STIX]{x1D6FC}\in (0,1))$
circle diffeomorphism with a break of size
$c\in \mathbb{R}_{+}\backslash \{1\}$
, with rotation number
$\unicode[STIX]{x1D70C}$
, is zero. This result cannot be extended to all irrational rotation numbers.
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