Vol. LXXXI, 2 (2012)
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

PDF                               Compressed Postscript                                 Version to read

Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

Telephone: + 421-2-60295111 Fax: + 421-2-65425882  
e-Mail:    Internet: