Solutions for the $p$-order Feigenbaum's functional equation $h(g(x))=g^{p}(h(x))$
Annales Polonici Mathematici, Tome 111 (2014) no. 2, pp. 183-195
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
This work deals with Feigenbaum's functional equation
$$\left\{
\begin{array}{l}
h(g(x))=g^p(h(x)),\\
g(0)=1, \quad -1\leq g(x)\leq1 ,\quad x\in[-1,1],
\end{array}
\right.
$$
where $p\geq 2$ is an integer, $g^p$ is the $p$-fold iteration of
$g$, and $h$ is a strictly monotone odd continuous function on
$[-1,1]$ with $h(0)=0$ and $|h(x)||x|$ ($x\in[-1,1]$, $x\neq 0$).
Using a constructive method, we discuss the existence of continuous
unimodal even solutions of the above equation.
Keywords:
work deals feigenbaums functional equation begin array x quad leq leq quad end array right where geq integer p fold iteration strictly monotone odd continuous function neq using constructive method discuss existence continuous unimodal even solutions above equation
Affiliations des auteurs :
Min Zhang 1 ; Jianguo Si 2
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author = {Min Zhang and Jianguo Si},
title = {Solutions for the $p$-order {Feigenbaum's} functional equation $h(g(x))=g^{p}(h(x))$},
journal = {Annales Polonici Mathematici},
pages = {183--195},
publisher = {mathdoc},
volume = {111},
number = {2},
year = {2014},
doi = {10.4064/ap111-2-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap111-2-6/}
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Min Zhang; Jianguo Si. Solutions for the $p$-order Feigenbaum's functional equation $h(g(x))=g^{p}(h(x))$. Annales Polonici Mathematici, Tome 111 (2014) no. 2, pp. 183-195. doi: 10.4064/ap111-2-6
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