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Showing 1 to 2 of 2 for “"horocycle flow"”.
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Transversals to horocycle flow on the moduli space of translation surfaces
… of saddle connections into return times under horocycle flow on the space of translation surfaces to a specific transversal. We show how to use this strategy to explicitly compute the distribution in the case of the octagon, the first case where the Veech group has multiple cusps, how to …
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Applications of dynamical systems to Farey sequences and continued fractions
… with utilizing the ergodic properties of the horocycle flow in SL(2,R) to study the spacing statistics of Farey fractions. For a given finite index subgroup H ⊆ SL(2,Z), we use a process developed by Fisher and Schmidt to lift a cross section of the horocycle flow on SL(2,R)/SL(2,Z) found by …