کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4637370 1340739 2006 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The topological entropy of nth iteration of an additive cellular automata
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
The topological entropy of nth iteration of an additive cellular automata
چکیده انگلیسی
In this paper, our aim is to investigate the topological entropy of nth iteration of an one-dimensional additive cellular automata (CA hereafter), i.e. the maps T:ZmZ→ZmZ which are given by Tx=(yn)n=-∞∞, yn=F(xn-r,…,xn+r)=∑i=-rrλixn+i(modm), x=(xn)n=-∞∞∈ZmZ and F:Zm2r+1→Zm, over Zm (m⩾2) by means of both the algorithm and Lyapunov exponents of the CA T that is given by D'amico et al. [Theor. Comput. Sci. 290 (2003) 1629-1646]. We show that if the local rule F is bipermutative (in Hedlund's terminology), then the topological entropy of nth iteration of one-dimensional additive CA is 2nr log m. We obtain necessary and sufficient conditions for the topological entropy of nth iteration of CA to be 2nr log m. We show that the uniform Bernoulli measure is a measure of maximal entropy for the nth iteration of the CA generated by bipermutative local rule F.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 174, Issue 2, 15 March 2006, Pages 1427-1437
نویسندگان
,