Fa角 di Bruno%26apos;s formula and nonhyperbolic fixed points of one-dimensional maps

作者:Vadim Ponomarenko
来源:International Journal of Mathematics and Mathematical Sciences, 2004.
DOI:10.1155/s0161171204306253

摘要

Fixed-point theory of one-dimensional maps of %26#8477; 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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