Plotting stable manifolds: Error estimates and noninvertible maps

Eric Kostelich, James A. Yorke, Zhiping You

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

A numerical procedure is described that can accurately compute the stable manifold of a saddle fixed point for a map of ℝ2, even if the map has no inverse. (Conventional algorithms use the inverse map to compute an approximation of the unstable manifold of the fixed point.) We rigorously analyze the errors that arise in the computation and guarantee that they are small. We also argue that a simpler, nonrigorous algorithm nevertheless produces highly accurate representations of the stable manifold.

Original languageEnglish (US)
Pages (from-to)210-222
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Volume93
Issue number3-4
DOIs
StatePublished - Jan 1 1996

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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