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Long and Short Periodic Billiard Trajectories in the Regular Pentagon

2021/11/18 by Samuel Everett, Everett, Samuel, Vanessa Lin +3
Computer Science · Mathematics · Physics and Astronomy · #37C83 #Algorithms and Data Compression #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2111.09856

openalex publication_date 2021/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In any periodic direction on the regular pentagon billiard table, there exists two combinatorially different billiard paths, with one longer than the other. For each periodic direction, McMullen asked if one could determine whether the periodic trajectory through a given point is long, short, or a saddle connection. In this paper we present an algorithm resolving this question for trajectories emanating from the midpoints of the pentagon.

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