Solutions for the p-order Feigenbaum’s functional equation $h\left(g\left(x\right)\right)=g^p\left(h\left(x\right)\right)$

Min Zhang, and Jianguo Si. "Solutions for the p-order Feigenbaum’s functional equation $h(g(x)) = g^{p}(h(x))$." Annales Polonici Mathematici 111.2 (2014): 183-195. <http://eudml.org/doc/280869>.

@article{MinZhang2014,
abstract = {This work deals with Feigenbaum’s functional equation ⎧ $h(g(x)) = g^p(h(x))$, ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 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 ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.},
author = {Min Zhang, Jianguo Si},
journal = {Annales Polonici Mathematici},
keywords = {Feigenbaum's functional equation; constructive method; continuous unimodal even solution},
language = {eng},
number = {2},
pages = {183-195},
title = {Solutions for the p-order Feigenbaum’s functional equation $h(g(x)) = g^\{p\}(h(x))$},
url = {http://eudml.org/doc/280869},
volume = {111},
year = {2014},
}

TY - JOUR
AU - Min Zhang
AU - Jianguo Si
TI - Solutions for the p-order Feigenbaum’s functional equation $h(g(x)) = g^{p}(h(x))$
JO - Annales Polonici Mathematici
PY - 2014
VL - 111
IS - 2
SP - 183
EP - 195
AB - This work deals with Feigenbaum’s functional equation ⎧ $h(g(x)) = g^p(h(x))$, ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 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 ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.
LA - eng
KW - Feigenbaum's functional equation; constructive method; continuous unimodal even solution
UR - http://eudml.org/doc/280869
ER -