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JMD

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 $\alpha$.

JMD

We study the dynamics of the geodesic and horocycle flows of the unit tangent bundle $(\hat M, T^1\mathfrak{F})$ of a compact minimal lamination $(M,\mathfrak{F})$ by negatively curved surfaces. We give conditions under which the action of the affine group generated by the joint action of these flows is minimal and examples where this action is not minimal. In the first case, we prove that if $\mathfrak{F}$ has a leaf which is not simply connected, the horocyle flow is topologically transitive.

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