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A generic-dimensional property of the invariant measures for circle diffeomorphisms

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  • Given any Liouville number $\alpha$, it is shown that the nullity of the Hausdorff dimension of the invariant measure is generic in the space of the orientation-preserving $C^\infty$ diffeomorphisms of the circle with rotation number $\alpha$.
    Mathematics Subject Classification: Primary: 37E10; Secondary: 37E45.


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