p. 221 - 226
Characterization of spacing shifts
with positive topological entropy
D. Ahmadi and M. Dabbaghian
Received: January 10, 2012; Accepted: June 29, 2012
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].
Keywords: entropy, proximal; D*-set; IP-set; density.
AMS Subject classification: Primary: 37B10; Secondary: 37B40, 37B20, 37B05
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