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A condition for zero entropy

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Abstract

Criteria for a homeomorphism of a compact metric space to have zero topological entropy are obtained. These are applied to show that minimal distal and POD flows have zero entropy. These notions are also relativized, and it is shown that entropy is preserved by the extensions they define.

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References

  1. J. Auslander,Minimal Flows and their Extensions, North-Holland Mathematical Studies, 153, 1988.

  2. H. Furstenberg, H. Keynes and L. Shapiro,Prime flows in topological dynamics, Isr. J. Math.14 (1973), 26–38.

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  3. W. Parry,Zero entropy of distal and related transformations, inTopological Dynamics: An International Symposium (J. Auslander and W. H. Gottschalk, ed.), W. A. Benjamin, New York, 1968, pp. 383–389.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    J. Auslander & K. Berg

Authors
  1. J. Auslander
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  2. K. Berg
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Auslander, J., Berg, K. A condition for zero entropy. Israel J. Math. 69, 59–64 (1990). https://doi.org/10.1007/BF02764729

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  • DOI: https://doi.org/10.1007/BF02764729

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