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- Title
Embedding minimal dynamical systems into Hilbert cubes.
- Authors
Gutman, Yonatan; Tsukamoto, Masaki
- Abstract
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.
- Subjects
DYNAMICAL systems; SHIFT systems; HARMONIC analysis (Mathematics); DIMENSION theory (Algebra); HILBERT transform; EMBEDDINGS (Mathematics); CUBES
- Publication
Inventiones Mathematicae, 2020, Vol 221, Issue 1, p113
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-019-00942-w