Geodesic
Characterization of spacing shifts with positive topological entropy
Acta mathematica Universitatis Comenianae, Tome 81 (2012) no. 2, pp. 221-226 
D. Ahmadi; M. Dabbaghian; D. Ahmadi; M. Dabbaghian. Characterization of spacing shifts with positive topological entropy. Acta mathematica Universitatis Comenianae, Tome 81 (2012) no. 2, pp. 221-226. http://geodesic.mathdoc.fr/item/AMUC_2012_81_2_a8/
@article{AMUC_2012_81_2_a8,
     author = {D. Ahmadi and M. Dabbaghian and D. Ahmadi and M. Dabbaghian},
     title = { Characterization of spacing shifts with positive topological entropy},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {221--226},
     year = {2012},
     volume = {81},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2012_81_2_a8/}
}
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Suppose P Í N and let (SPsP) be the spacing shift defined by P. We show that if the topological entropy h(sP) of a spacing shift is equal zero, then (SPsP) 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].