Embedding minimal dynamical systems into Hilbert cubes

Yonatan Gutman, Masaki Tsukamoto

研究成果: Contribution to journalArticle査読

2 被引用数 (Scopus)

抄録

We study the problem of embedding minimal dynamical systems into the shift action on the Hilbert cube ([0,1]N)Z. 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 ([0,1]N)Z, 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.

本文言語英語
ページ(範囲)113-166
ページ数54
ジャーナルInventiones Mathematicae
221
1
DOI
出版ステータス出版済み - 7 1 2020

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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