Characterization of Spacing Shifts with Positive Topological Entropy
نویسنده
چکیده
Suppose P ⊆ N and let (ΣP , σP ) be the spacing shift defined by P . We show that if the topological entropy h(σP ) of a spacing shift is equal zero, then (ΣP , σP ) is proximal. Also h(σP ) = 0 if and only if P = N \ E where E is an intersective set. Moreover, we show that h(σP ) > 0 implies that P is a ∆ ∗-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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تاریخ انتشار 2012