Bifurcations of periodic solutions for plane mappings
type: Item
instance of: scholarly article
title: Bifurcations of periodic solutions for plane mappings
zbMATH Open document ID: 0789.58054
DOI: 10.1007/BF02457483
author: Qiong Li
author: Jinde Cao
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1994-06-13T00:00:00Z
review text: The authors investigate the Taylor mapping \[ F_ A: \begin{cases} x_ 1 = 2x-y+A\sin x\\y_ 1 = x\end{cases} \] for \(A\in (4,3/2\pi]\). They prove that for such \(F_ A\) there exists a regular homoclinic point. This implies the existence of infinitely many periodic points. Earlier, an analogous result for \(A\in (3/2 \pi,\infty)\) was obtained by Zhu Si-ming and others. Similar assertion for the mapping describing the motion of a bouncing ball is also true.
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 480417
zbMATH Keywords: periodic solutions
zbMATH Keywords: plane mappings
zbMATH Keywords: bifurcation
zbMATH Keywords: Taylor mapping
reviewed by: Yu. N. Bibikov
MaRDI profile type: Publication
cites work: Homoclinic bifurcations and the area-conserving Henon mapping
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
full work available at URL: https://doi.org/10.1007/bf02457483
OpenAlex ID: W41798881
description: scientific article; zbMATH DE number 480417