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Horocycle flows without minimal sets

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 Added by Shigenori Matsumoto
 Publication date 2014
  fields
and research's language is English




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We show that the horocycle flows of open tight hyperbolic surfaces do not admit minimal sets.



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160 - Shigenori Matsumoto 2014
We show that the horocycle flow associated with a foliation on a compact manifold by hyperbolic surfaces is minimal under certain conditions.
We study the dynamics of the geodesic and horocycle flows of the unit tangent bundle $(hat M, T^1mathcal{F})$ of a compact minimal lamination $(M,mathcal F)$ 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 $mathcal F$ has a leaf which is not simply connected, the horocyle flow is topologically transitive.
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