An iteration problem
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...
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Institute of Physics Publishing (UK)
2013
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/32609/ http://irep.iium.edu.my/32609/1/1742-6596_435_1_012007.pdf |
| _version_ | 1848780592531898368 |
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| author | Bekbaev, Ural |
| author_facet | Bekbaev, Ural |
| author_sort | Bekbaev, Ural |
| building | IIUM Repository |
| collection | Online Access |
| description | 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.
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| first_indexed | 2025-11-14T15:36:07Z |
| format | Article |
| id | iium-32609 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T15:36:07Z |
| publishDate | 2013 |
| publisher | Institute of Physics Publishing (UK) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-326092013-11-08T02:43:58Z http://irep.iium.edu.my/32609/ An iteration problem Bekbaev, Ural QA Mathematics 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. Institute of Physics Publishing (UK) 2013 Article PeerReviewed application/pdf en http://irep.iium.edu.my/32609/1/1742-6596_435_1_012007.pdf Bekbaev, Ural (2013) An iteration problem. Journal of Physics: Conference Series, 435. pp. 1-4. ISSN 1742-6588 (P), 1742-6596 (O) |
| spellingShingle | QA Mathematics Bekbaev, Ural An iteration problem |
| title | An iteration problem |
| title_full | An iteration problem |
| title_fullStr | An iteration problem |
| title_full_unstemmed | An iteration problem |
| title_short | An iteration problem |
| title_sort | iteration problem |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/32609/ http://irep.iium.edu.my/32609/1/1742-6596_435_1_012007.pdf |