Hausdorff dimension of invariant measure of circle diffeomorphisms with a break point
Konstantin KhaninDepartment of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON, Canada M5S 2E4 emailSaša KocićDepartment of Mathematics, University of Mississippi, PO Box 1848, University, MS 38677-1848, USA email
2017en
ABI
Annotatsiya
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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