A generic dimensional property of the invariant measures for circle diffeomorphisms

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

2011-01-24

arxiv.org/abs/1101.4463v2

Mathematics

Dynamical Systems

9 pages

Scientific paper

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 $\alpha$.

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