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Abstract
In this paper we show how the notion of mean dimension is connected in a natural way to the following two questions: what points in a dynamical system (X, T) can be distinguished by factors with arbitrarily small topological entropy, and when can a system (X, T) be embedded in (([0, 1]d)Z, shift). Our results apply to extensions of minimalZ-actions, and for this case we also show that there is a very satisfying dimension theory for mean dimension.
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Author information
Elon Lindenstrauss
Present address: Institute for Advanced Study, 08540, Princeton, N.J.
Authors and Affiliations
Institute of Mathematics, the Hebrew University, 91904, Jerusalem, Israel
Elon Lindenstrauss
- Elon Lindenstrauss
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Lindenstrauss, E. Mean dimension, small entropy factors and an embedding theorem.Publications Mathématiques de L’Institut des Hautes Scientifiques89, 227–262 (1999). https://doi.org/10.1007/BF02698858
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