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Horocycle flow orbits and lattice surface characterizations
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Horocycle flow orbits and lattice surface characterizations
classification
math.DS
keywords
flowcharacterizationsclosurehorocyclelatticeorbitsurfacealmost
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The orbit closure of any translation surface under the horocycle flow in almost any direction equals its $SL_2(\mathbb{R})$ orbit closure. This result gives rise to new characterizations of lattice surfaces in terms of the hororcycle flow.
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