Vadim Ponomarenko, "Faà di Bruno's formula and nonhyperbolic fixed points of one-dimensional maps", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 676909, 7 pages, 2004. https://doi.org/10.1155/S0161171204306253
Faà di Bruno's formula and nonhyperbolic fixed points of one-dimensional maps
Fixed-point theory of one-dimensional maps of 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 are exhibited such that the Maclaurin series of and are identical.
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