In this paper we present some results and applications of a new invariant for dynamical systems that can be viewed as a dynamical analogue of topological dimension. This invariant has been introduced by M. Gromov, and enables one to assign a meaningful quantity to dynamical systems of infinite topological dimension and entropy. We also develop an alternative approach that is metric dependent and is intimately related to topological entropy.
KeywordsTopological Dimension Open Cover Finite Subset Amenable Group Topological Entropy
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- W. Hurewicz and H. Wallman,Dimension Theory, Princeton University Press, 1941.Google Scholar
- A. Jaworski, Ph.D. thesis, University of Maryland, 1974.Google Scholar
- E. Lindenstrauss,Mean dimension, small entropy factors and an imbedding theorem, preprint.Google Scholar