The Falkner-Skan equation. I: The creation of strange invariant sets
type: Item
instance of: scholarly article
title: The Falkner-Skan equation. I: The creation of strange invariant sets
zbMATH Open document ID: 0828.34028
author: Colin Sparrow
author: Peter Swinnerton-Dyer
published in: Journal of Differential Equations
publication date: 1995-09-18T00:00:00Z
review text: The paper contains a detailed study of bifurcations in the Falkner-Skan equation \[ y'''+ y'' y+ \lambda(1- (y')^2)= 0\tag{1} \] for values \(\lambda> 0\). The authors show the machinery of these bifurcations which lead to the birth of complicated invariant sets of (1) and occur as \(\lambda\) increases through positive integer values. In particular, an almost complete account of the creation of the most interesting admissible solutions (for those \(\sup_{x\in R} |y'(x)|< \infty)\) by bifurcations from two trajectories \(y'= \pm 1\) is given. Although the equation (1) has the symmetry properties (it is reversible by Sevryuk), the authors do not make essential use of this symmetry in their investigation. One may state that a new codimension one bifurcation phenomenon in general parametrized families of differential equations is discovered in this paper. It is worth pointing out that the most part of this well written work is self-contained.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 784944
zbMATH Keywords: orbits
zbMATH Keywords: periodic solution
zbMATH Keywords: bifurcations
zbMATH Keywords: Falkner-Skan equation
zbMATH Keywords: complicated invariant sets
reviewed by: Elena Trofimchuk
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1094
OpenAlex ID: W2015695491
DOI: 10.1006/JDEQ.1995.1094
description: scientific article; zbMATH DE number 784944