Homoclinic shadowing

Brian A. Coomes, Hüseyin Koçak, Kenneth J. Palmer

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

A new method for rigorously establishing the existence of a transversal homoclinic orbit to a periodic orbit (or a fixed point) of diffeomorphisms in R n is presented. It is a computer-assisted technique with two main components. First, a global Newton's method is devised to compute a suitable pseudo (approximate) homoclinic orbit to a pseudo periodic orbit. Then, a homoclinic shadowing theorem, which is proved herein, is invoked to establish the existence of a true transversal homoclinic orbit to a true periodic orbit near these pseudo orbits.

Original languageEnglish (US)
Pages (from-to)175-215
Number of pages41
JournalJournal of Dynamics and Differential Equations
Volume17
Issue number1
DOIs
StatePublished - Jan 1 2005

Keywords

  • Chaos
  • Newton's method
  • Pseudo orbits
  • Shadowing
  • Transversal homoclinic orbits

ASJC Scopus subject areas

  • Analysis

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