Coding of billiards in hyperbolic 3-space

Singh, Phool

doi:10.48550/arxiv.2009.14427

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2021

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“…Another natural question is whether a version of Billiard Rigidity Theorem holds in higher dimensions. Coding billiards in three-dimensional hyperbolic polyhedra was considered in [Sin20].…”

Section: Connection To Prior Results and Questionsmentioning

confidence: 99%

Hyperbolic cone metrics and billiards

Erlandsson¹,

Leininger²,

Sadanand³

2021

Preprint

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A negatively curved hyperbolic cone metric is called rigid if it is determined (up to isotopy) by the support of its Liouville current, and flexible otherwise. We provide a complete characterization of rigidity and flexibility, prove that rigidity is a generic property, and parameterize the associated deformation space for any flexible metric. As an application, we parameterize the space of hyperbolic polygons with the same symbolic coding for their billiard dynamics, and prove that generically this parameter space is a point.

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Section: Connection To Prior Results and Questionsmentioning

confidence: 99%