Faà di Bruno's formula and nonhyperbolic fixed points of one-dimensional maps

Vadim Ponomarenko

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-7

Abstract:

Fixed-point theory of one-dimensional maps of 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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:676909

DOI: 10.1155/S0161171204306253

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