The calculation of resonance separatrices for the near-integrable case of the standard mapping
type: Item
instance of: scholarly article
title: The calculation of resonance separatrices for the near-integrable case of the standard mapping
zbMATH Open document ID: 0668.70029
DOI: 10.1007/BF00945123
author: Michael P. Mortell
author: Brian R. Seymour
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1988-01-01T00:00:00Z
review text: The standard mapping arises in many physical applications, including the analysis of nonlinear resonant acoustic oscillations in a closed tube. A perturbation expansion, in powers of the amplitude parameter, is given for the calculation of the fixed points of various orders and the associated separatrices. It is shown how exact homoclinic orbits can be calculated numerically. Explicit analytic expressions are given for the separatrices associated with the first four resonances when the perturbation parameter is small.
Mathematics Subject Classification ID: 70K30
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 4094910
zbMATH Keywords: standard mapping
zbMATH Keywords: nonlinear resonant acoustic oscillations in a closed tube
zbMATH Keywords: perturbation expansion
zbMATH Keywords: fixed points
zbMATH Keywords: separatrices
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00945123
OpenAlex ID: W2244415795
description: scientific article; zbMATH DE number 4094910