Geometric methods for computing invariant manifolds
type: Item
instance of: scholarly article
title: Geometric methods for computing invariant manifolds
zbMATH Open document ID: 0834.65056
DOI: 10.1016/0168-9274(95)00037-U
author: Gerald Moore
published in: Applied Numerical Mathematics
publication date: 1996-04-10T00:00:00Z
review text: The purpose of this paper is to contrast the different algorithms obtained for various invariant manifolds when different parametrisations are used. After choosing an appropriate parametrisation for a given type of invariant manifolds, a system of equations is constructed which the representation with respect to this parametrisation must satisfy. Hence, different methods are obtained for computing the invariant manifolds. The author considers one-dimensional manifolds (periodic orbits, connecting orbits between stationary solutions, and stable manifolds of fixed points), and two-dimensional ones (invariant tori for autonomous systems, invariant curves for periodically forced systems, and stable manifolds of fixed points).
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 37C80
Mathematics Subject Classification ID: 37N99
Mathematics Subject Classification ID: 70G10
Mathematics Subject Classification ID: 34D35
zbMATH DE Number: 803530
zbMATH Keywords: periodic orbits
zbMATH Keywords: invariant tori
zbMATH Keywords: algorithms
zbMATH Keywords: invariant manifolds
zbMATH Keywords: parametrisation
zbMATH Keywords: connecting orbits
zbMATH Keywords: stable manifolds of fixed points
zbMATH Keywords: autonomous systems
zbMATH Keywords: invariant curves
zbMATH Keywords: stable manifolds
reviewed by: Andrzej Marciniak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 803530