Bünyamin Aydin

Cumhuriyet University, Sivas, Turkey. Tel: 90-346-2191010 -(1890), Fax:90-346-2191224, E-mail: [email protected]

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

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, h_T(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 h_T(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.

MSC 2000 codes: primary 26A18; 54h20.