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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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  • [1]

    B. Fayad and M. Saprykina, Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary, Ann. Sci. École Norn. Sup. (4), 38 (2005), 339-364.doi: 10.1016/j.ansens.2005.03.004.

    [2]

    M.-R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Inst. Hautes Études Sci. Publ. Math., 49 (1979), 5-233.

    [3]

    S. Matsumoto, Dense properties of the space of circle diffeomorphisms with a Liouville rotation number, Nonlinearity, 25 (2012), 1495-1511.doi: 10.1088/0951-7715/25/5/1495.

    [4]

    V. Sadovskaya, Dimensional characteristics of invariant measures for circle diffeomorphisms, Ergodic Theory Dynam. Systems, 29 (2009), 1979-1992.doi: 10.1017/S0143385708000916.

    [5]

    J.-C. Yoccoz, Conjugaison différentiable des difféimorphismes du cercle dont le nombre de rotation vérifie une conditon diophantienne, Ann. Sci. Ecole Norm. Sup. (4), 17 (1984), 333-359.

    [6]

    J.-C. Yoccoz, Centralisateurs et conjugaison différentiable des difféomorphismes du cercle, Astérisque, 231 (1995), 89-242.

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