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 (S_{P} s_{P})
be the spacing shift defined by P. We show that if the topological entropy
h(s_{P})
of a spacing shift is equal zero, then
(S_{P} s_{P})
is proximal. Also
h(s_{P}) = 0
if and only if
P = N - E. where E is an intersective set. Moreover, we show that
h(s_{P}) > 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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