On the dynamic behaviour of Chebyshev polynomials (Q1891322)
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scientific article; zbMATH DE number 759477
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the dynamic behaviour of Chebyshev polynomials |
scientific article; zbMATH DE number 759477 |
Statements
On the dynamic behaviour of Chebyshev polynomials (English)
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30 May 1995
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Generalizing well-known results concerning the chaotic behaviour of the Feigenbaum function \(f(x)= 4x(1- x)\) on \([0,1]\) (which is conjugated to the Chebyshev polynomial of second degree) the number of \(k\)-periodic points of the Chebyshev polynomial \(T_ n\) of degree \(n> 1\) is determined and it is proved that all the fixed points and all the cycles of \(T_ n\) are unstable.
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chaos
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Feigenbaum function
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periodic point
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inclusion-exclusion- principle
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stability
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Chebyshev polynomial
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