Embedding minimal dynamical systems into Hilbert cubes

• 成果类型: Article
• 署名作者: Gutman, Yonatan; Tsukamoto, Masaki
• 署名单位: Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Kyushu University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00942-w
• 发表日期: 2020
• 页码: 113-166
• 关键词: mean dimension; morphisms; shifts

摘要

We study the problem of embedding minimal dynamical systems into the shift action on the Hilbert cube mml:mfenced close=) open=([0,1]NZ\ This problem is intimately related to the theory of mean dimension, which counts the average number of parameters for describing a dynamical system. Lindenstrauss proved that minimal systems of mean dimension less than cN for c=1/36 can be embedded in mml:mfenced close=) open=([0,1]NZ and asked what is the optimal value for c. We solve this problem by showing embedding is possible when c=1/2 The value c=1/2 is optimal. The proof exhibits a new interaction between harmonic analysis and dynamical coding techniques.