TWO-SIDED SHIFT SPACES OVER INFINITE ALPHABETS

Ott, Tomforde and Willis proposed a useful compactification for one-sided shifts over infinite alphabets. Building from their idea, we develop a notion of two-sided shift spaces over infinite alphabets, with an eye towards generalizing a result of Kitchens. As with the one-sided shifts over infinite...

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Bibliographic Details
Published in:Journal of the Australian Mathematical Society (2001) 2017-12, Vol.103 (3), p.357-386
Main Authors: GONÇALVES, DANIEL, SOBOTTKA, MARCELO, STARLING, CHARLES
Format: Article
Language:English
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Summary:Ott, Tomforde and Willis proposed a useful compactification for one-sided shifts over infinite alphabets. Building from their idea, we develop a notion of two-sided shift spaces over infinite alphabets, with an eye towards generalizing a result of Kitchens. As with the one-sided shifts over infinite alphabets, our shift spaces are compact Hausdorff spaces but, in contrast to the one-sided setting, our shift map is continuous everywhere. We show that many of the classical results from symbolic dynamics are still true for our two-sided shift spaces. In particular, while for one-sided shifts the problem about whether or not any $M$ -step shift is conjugate to an edge shift space is open, for two-sided shifts we can give a positive answer for this question.
ISSN:1446-7887
1446-8107
DOI:10.1017/S1446788717000039