Journal of Modern Dynamics (JMD)

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

Pages: 553 - 563, Issue 4, December 2013      doi:10.3934/jmd.2013.7.553

       Abstract        References        Full Text (147.7K)       Related Articles       

Shigenori Matsumoto - Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda, Surugadai, Chiyoda-ku, Tokyo, 101-8308, Japan (email)

Abstract: 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 $\alpha$.

Keywords:  Circle diffeomorphism, rotation number, Liouville number, Hausdorff dimension, invariant measure, fast approximation by conjugation.
Mathematics Subject Classification:  Primary: 37E10; Secondary: 37E45.

Received: December 2012;      Revised: December 2013;      Available Online: March 2014.