A generic dimensional property of the invariant measures for circle diffeomorphisms

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 $\alpha$.

9 pages

Cited by in corpus (1)

• Dense properties of the space of the circle diffeomorphisms with a Liouville rotation number