Cutting sequences on Bouw-Möller surfaces: an S-adic characterization

Davis, Diana; Pasquinelli, Irene; Ulcigrai, Corinna

doi:10.48550/arxiv.1509.03905

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Directions To Saddle Connection Vectors On the Golden L1

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2018

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“…Finally, we note that in the substitution rules in Definition 3.8, we have combined "derivation" and "normalization" (see [DPU18,§7]) into one step. Namely, given a cutting sequence that corresponds to a path on transition diagram D, running it through any of the substitutions r i yields a cutting sequence that also corresponds to a path on transition diagram D, in a single step.…”

Section: Directions To Saddle Connection Vectors On the Golden Lmentioning

confidence: 99%

Periodic paths on the pentagon, double pentagon and golden L

Davis¹,

Lelièvre²

2018

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We give a tree structure on the set of all periodic directions on the golden L, which gives an associated tree structure on the set of periodic directions for the pentagon billiard table and double pentagon surface. We use this to give the periods of periodic directions on the pentagon and double pentagon. We also show examples of many periodic billiard trajectories on the pentagon, which are strikingly beautiful, and we describe some of their properties. Finally, we give conjectures and future directions based on experimental computer evidence.

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Section: Directions To Saddle Connection Vectors On the Golden Lmentioning

confidence: 99%