International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 676909 | https://doi.org/10.1155/S0161171204306253

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

Received22 Jun 2003

Abstract

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 f are exhibited such that the Maclaurin series of f(f(x)) and x are identical.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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