A strongly aperiodic set of tiles in the hyperbolic plane

• 成果类型: Article
• 署名作者: Goodman-Strauss, C
• 署名单位: University of Arkansas System; University of Arkansas Fayetteville
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0384-1
• 发表日期: 2005
• 页码: 119-132
• 关键词: tilings

摘要

We construct the first known example of a strongly aperiodic set of tiles in the hyperbolic plane. Such a set of tiles does admit a tiling, but admits no tiling with an infinite cyclic symmetry. This can also be regarded as a regular production system [5] that does admit bi-infinite orbits, but admits no periodic orbits.