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Follower, predecessor, and extender entropies

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Abstract

Using the follower/predecessor/extender set sequences defined by the first author, we define quantities which we call the follower/predecessor/extender entropies, which can be associated to any shift space. We analyze the behavior of these quantities under conjugacies and factor maps, most notably showing that extender entropy is a conjugacy invariant and that having follower entropy zero is a conjugacy invariant. We give some applications, including examples of shift spaces with equal entropy which can be distinguished by extender entropy, and examples of shift spaces which can be shown to not be isomorphic to their inverse by using follower/predecessor entropy.

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Authors and Affiliations

  1. Department of Mathematics, University of Denver, 2390 S. York St., Denver, CO, 80208, USA

    Thomas French & Ronnie Pavlov

Authors
  1. Thomas French
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  2. Ronnie Pavlov
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Corresponding author

Correspondence to Ronnie Pavlov.

Additional information

Communicated by H. Bruin.

The second author gratefully acknowledges the support of NSF Grant DMS-1500685.

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French, T., Pavlov, R. Follower, predecessor, and extender entropies. Monatsh Math 188, 495–510 (2019). https://doi.org/10.1007/s00605-018-1224-5

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  • DOI: https://doi.org/10.1007/s00605-018-1224-5

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