# An iteration problem

Bekbaev, Ural (2013) An iteration problem. Journal of Physics: Conference Series, 435. pp. 1-4. ISSN 1742-6588 (P), 1742-6596 (O)

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## Abstract

Let F stand for the feld of real or complex numbers, \phi : F^n\rightarrow F^n be any given polynomial map of the form \phi(x) = x + "higher order terms". We attach to it the following operator D : F[x]\rightarrow F[x] defined by D(f) = f-f\circle\phi, where F[x] = F[x_1; x_2; ...; x_n]- the F-algebra of polynomials in variables x_1; x_2;...; x_n, f \in F[x] and \circle stands for the composition(superposition) operation. It is shown that trajectory of any f\in F[x] tends to zero, with respect to a metric, and stabilization of all trajectories is equivalent to the stabilization of trajectories of x_1; x_2;...; x_n.

Item Type: Article (Journal) 6830/32609 Q Science > QA Mathematics Kulliyyah of Engineering > Department of Science Associate Prof. Ural Bekbaev 08 Nov 2013 10:43 08 Nov 2013 10:43 http://irep.iium.edu.my/id/eprint/32609

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