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 |
| Summary: | 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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