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Characterization of spacing shifts with positive topological entropy

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Author(s): D. Ahmadi | M. Dabbaghian

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXI;
Issue: 2;
Start page: 221;
Date: 2012;
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Keywords: Entropy | proximal | D *-set | IP-set | density

ABSTRACT
Suppose P Í N and let (SP sP) be the spacing shift defined by P. We show that if the topological entropy h(sP) of a spacing shift is equal zero, then (SP sP) is proximal. Also h(sP) = 0 if and only if P = N - E. where E is an intersective set. Moreover, we show that h(sP) > 0 implies that P is a D*-set; and by giving a class of examples, we show that this is not a sufficient condition. Using these results we solve question 5 given in [J. Banks et al.,Dynamics of Spacing Shifts, Discrete Contin. Dyn. Syst.,to appear].
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