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This paper was retracted on 21 February 2014, see Entropy 2014, 16(2), 1122.

Entropy 2004, 6(2), 257-261; doi:10.3390/e6020257
Article

Statistical Convergent Topological Sequence Entropy Maps of the Circle

Received: 26 August 2003 / Accepted: 17 December 2003 / Published: 19 March 2004
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Abstract

A continuous map f of the interval is chaotic iff there is an increasing of nonnegative integers T such that the topological sequence entropy of f relative to T, hT(f), is positive [4]. On the other hand, for any increasing sequence of nonnegative integers T there is a chaotic map f of the interval such that hT(f)=0 [7]. We prove that the same results hold for maps of the circle. We also prove some preliminary results concerning statistical convergent topological sequence entropy for maps of general compact metric spaces.
Keywords: Statistical convergent; topological sequence; entropy; sequence entropy Statistical convergent; topological sequence; entropy; sequence entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Aydin, B. Statistical Convergent Topological Sequence Entropy Maps of the Circle. Entropy 2004, 6, 257-261.

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