Homoclinic shadowing

Brian A Coomes, Huseyin Kocak, Kenneth J. Palmer

Research output: Contribution to journalArticle

18 Citations (Scopus)

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 2005

Fingerprint

Shadowing
Homoclinic
Homoclinic Orbit
Periodic Orbits
Diffeomorphisms
Newton Methods
Orbit
Fixed point
Theorem

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Homoclinic shadowing. / Coomes, Brian A; Kocak, Huseyin; Palmer, Kenneth J.

In: Journal of Dynamics and Differential Equations, Vol. 17, No. 1, 01.2005, p. 175-215.

Research output: Contribution to journalArticle

Coomes, Brian A ; Kocak, Huseyin ; Palmer, Kenneth J. / Homoclinic shadowing. In: Journal of Dynamics and Differential Equations. 2005 ; Vol. 17, No. 1. pp. 175-215.
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