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Retraction published on 21 February 2014, see Entropy 2014, 16(2), 1122.

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

Statistical Convergent Topological Sequence Entropy Maps of the Circle

Cumhuriyet University, Sivas, Turkey
Received: 26 August 2003 / Accepted: 17 December 2003 / Published: 19 March 2004
Download PDF [18 KB, 24 February 2015; original version 24 February 2015]

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 (CC BY 3.0).

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

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