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Properties of Shadowable Points: Chaos and Equicontinuity

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Abstract

We extend the study on shadowable points recently introduced by Morales in relation to chaotic or non-chaotic properties. Firstly, some sufficient conditions for a quantitative shadowable point to be approximated by an entropy point are given. As a corollary, we get different three chaotic conditions from which a shadowable point becomes an entropy point. Secondly, we provide a dichotomy on the interior of the set of shadowable chain recurrent points by two canonical chaotic and non-chaotic dynamics, the full shift and odometers.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, Komaba Meguro, Tokyo, 153-8914, Japan

    Noriaki Kawaguchi

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  1. Noriaki Kawaguchi
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Correspondence to Noriaki Kawaguchi.

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Kawaguchi, N. Properties of Shadowable Points: Chaos and Equicontinuity. Bull Braz Math Soc, New Series 48, 599–622 (2017). https://doi.org/10.1007/s00574-017-0033-0

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  • DOI: https://doi.org/10.1007/s00574-017-0033-0

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