Faà di Bruno's formula and nonhyperbolic fixed points of one-dimensional maps (Q1774773)
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scientific article; zbMATH DE number 2168705
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Faà di Bruno's formula and nonhyperbolic fixed points of one-dimensional maps |
scientific article; zbMATH DE number 2168705 |
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Faà di Bruno's formula and nonhyperbolic fixed points of one-dimensional maps (English)
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18 May 2005
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Summary: Fixed-point theory of one-dimensional maps of \(\mathbb{R}\) does not completely address the issue of nonhyperbolic fixed-points. This note generalizes the existing tests to completely classify all such fixed-points. To do this, a family of operators are exhibited that are analogous to generalizations of the Schwarzian derivative. In addition, a family of functions \(f\) are exhibited such that the MacLaurin series of \(f(f(x))\) and \(x\) are identical.
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fixed-point theory
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generalized Schwarzian-type derivatives
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iteration
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classification of fixed-points
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0.9049794
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0.8842223
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0.87465054
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0.86685187
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0.86264503
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0.85827696
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0.85786414
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