Bifurcation of periodic orbits near a frequency maximum in near- integrable driven oscillators with friction
type: Item
instance of: scholarly article
title: Bifurcation of periodic orbits near a frequency maximum in near- integrable driven oscillators with friction
zbMATH Open document ID: 0778.70017
DOI: 10.1007/BF00914356
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1993-05-16T00:00:00Z
review text: (From authors' abstract.) The authors investigate analytically the effect of perturbations on an integrable oscillator with one degree of freedom whose frequency shows a maximum as a function of the energy, i.e. a system with nonmonotone twist. The perturbation depends on three parameters: friction, variation of the frequency, strength of the driving force. The main result is the appearance of two chains of saddle node pairs in the phase portrait. This contrasts with the bifurcation of one chain of periodic orbits in the case of perturbations of monotone twist systems. The result is obtained for a mapping, but it is demonstrated that the same formalism and results apply for time continuous systems as well.
Mathematics Subject Classification ID: 70K40
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 168466
zbMATH Keywords: perturbations
zbMATH Keywords: nonmonotone twist
zbMATH Keywords: saddle node pairs
zbMATH Keywords: phase portrait
author: Theo P. Valkering
author: Stephan A. van Gils
reviewed by: E. Brommundt
MaRDI profile type: Publication
cites work: Regular and stochastic motion
cites work: The birth of twin Poincaré-Birkhoff chains near 1:3 resonance
cites work: The birth process of periodic orbits in non-twist maps
cites work: Stochastic webs
cites work: On the existence of infinite period-doubling sequences in a class of 4D semi-symplectic mappings
full work available at URL: https://doi.org/10.1007/bf00914356
OpenAlex ID: W1968077278
description: scientific article; zbMATH DE number 168466