Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems

Yasuaki Hiraoka

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The algorithm of our method is explained in detail by dividing into four steps. An application to a two dimensional reversible system is also treated and the existence of a symmetric homoclinic orbit is rigorously verified as an example.

Original languageEnglish
Pages (from-to)797-806
Number of pages10
JournalKybernetika
Volume43
Issue number6
Publication statusPublished - 2007 Dec 1

Keywords

  • Exponential dichotomy
  • Homoclinic orbits
  • Rigorous numerics

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Information Systems
  • Artificial Intelligence
  • Electrical and Electronic Engineering

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