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Billiards in ideal hyperbolic polygons

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  • We consider billiard trajectories in ideal hyperbolic polygons and present a conjecture about the minimality of the average length of cyclically related billiard trajectories in regular hyperbolic polygons. We prove this conjecture in particular cases, using geometric and algebraic methods from hyperbolic geometry.
    Mathematics Subject Classification: Primary: 37D40, 53A35; Secondary: 37C27.

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