On the Feigenbaum's functional equation \(f^ p(\lambda x)=\lambda f(x)\)
type: Item
instance of: scholarly article
title: On the Feigenbaum's functional equation \(f^ p(\lambda x)=\lambda f(x)\)
zbMATH Open document ID: 0805.39009
author: Gongfu Liao
published in: Chinese Annals of Mathematics. Series B
publication date: 1994-07-07T00:00:00Z
review text: The author considers the generalization of Feigenbaum's functional equation \(f^ p (\lambda x) = \lambda f(x)\), where \(p \geq 2\) is an integer, \(x \in [-1,1]\), \(f^ p\) denotes the \(p\)-fold iteration of \(f\), \(\lambda \in (0,1)\) is to be determined and \(f(0) = 1\), \(-1 \leq f(x) \leq 1\). For the case \(p=2\) the existence of even unimodal \(C^ 1\) solution is well-known, the case \(p=3\) was recently studied and the author's results give a feasible method to construct even unimodal \(C^ 1\) solutions for any \(p \geq 2\). Other classes of solutions like continuous single-valley solutions or piecewise smooth single-valley solutions are studied.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 589871
zbMATH Keywords: even unimodal \(C^ 1\) solution
zbMATH Keywords: Feigenbaum's functional equation
zbMATH Keywords: single-valley solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 589871