Feigenbaum theory for unimodal maps with asymmetric critical point: rigorous results
type: Item
instance of: scholarly article
title: Feigenbaum theory for unimodal maps with asymmetric critical point: rigorous results
zbMATH Open document ID: 0921.58037
published in: Communications in Mathematical Physics
publication date: 1999-09-30T00:00:00Z
review text: The subject of this paper deals with functional equations of the Feigenbaum type which occur in the theory of period-doubling cascades for families of unimodal maps \(f\) of an interval with a single critical point of degree \(d\) and which has differing left and right \(d\)-th derivative at a critical point. The authors apply the methods of H. Epstein to prove the existence of a line of period-2 solutions of the Feigenbaum period-doubling renormalisation transformation. These solutions govern the universal behaviour of families of unimodal maps with ``asymmetric critical points'' of degree \(d\).
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 1294552
zbMATH Keywords: asymmetric critical points
zbMATH Keywords: functional equations of Feigenbaum type
zbMATH Keywords: period-doubling cascades
zbMATH Keywords: unimodal maps
zbMATH Keywords: renormalization
author: B. D. Mestel
author: A. H. Osbaldestin
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s002200050448
OpenAlex ID: W2066003546
DOI: 10.1007/S002200050448
description: scientific article; zbMATH DE number 1294552