Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse

J.P. England, B. Krauskopf, H.M. Osinga

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We present an algorithm to compute the one-dimensional stable manifold of a saddle point for a planar map. In contrast to current standard techniques, here it is not necessary to know the inverse or approximate it, for example, by using Newton's method. Rather than using the inverse, the manifold is grown starting from the linear eigenspace near the saddle point by adding a point that maps back onto an earlier segment of the stable manifold. The performance of the algorithm is compared to other methods using an example in which the inverse map is known explicitly. The strength of our method is illustrated with examples of noninvertible maps, where the stable set may consist of many different pieces, and with a piecewise-smooth model of an interrupted cutting process. The algorithm has been implemented for use in the DsTool environment and is available for download with this paper.
Original languageEnglish
Pages (from-to)161-190
JournalSIAM Journal on Applied Dynamical Systems
Volume3
Issue number2
DOIs
Publication statusPublished - 2004

Bibliographical note

Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse

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