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...
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| Format: | Article |
| Language: | English |
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Institute of Physics Publishing (UK)
2013
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| Online Access: | http://irep.iium.edu.my/32609/ http://irep.iium.edu.my/32609/1/1742-6596_435_1_012007.pdf |
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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) |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Bekbaev, Ural An iteration problem |
| 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.
|
| format |
Article |
| author |
Bekbaev, Ural |
| author_facet |
Bekbaev, Ural |
| author_sort |
Bekbaev, Ural |
| title |
An iteration problem |
| title_short |
An iteration problem |
| title_full |
An iteration problem |
| title_fullStr |
An iteration problem |
| title_full_unstemmed |
An iteration problem |
| title_sort |
iteration problem |
| publisher |
Institute of Physics Publishing (UK) |
| publishDate |
2013 |
| url |
http://irep.iium.edu.my/32609/ http://irep.iium.edu.my/32609/1/1742-6596_435_1_012007.pdf |
| first_indexed |
2023-09-18T20:47:04Z |
| last_indexed |
2023-09-18T20:47:04Z |
| _version_ |
1777409745522524160 |