Advanced Search
Article Contents
Article Contents

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

Abstract / Introduction Related Papers Cited by
  • 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.


    \begin{equation} \\ \end{equation}
  • [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.


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


    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.


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


    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.


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

  • 加载中

Article Metrics

HTML views() PDF downloads(77) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint