Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems

Yasuaki Hiraoka

Kybernetika (2007)

  • Volume: 43, Issue: 6, page 797-806
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Hiraoka, Yasuaki. "Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems." Kybernetika 43.6 (2007): 797-806. <http://eudml.org/doc/33897>.

@article{Hiraoka2007,
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.},
author = {Hiraoka, Yasuaki},
journal = {Kybernetika},
keywords = {rigorous numerics; exponential dichotomy; homoclinic orbits; numerical examples; exponential dichotomy; homoclinic orbits; reversible dynamical systems; Melnikov functions; algorithm},
language = {eng},
number = {6},
pages = {797-806},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems},
url = {http://eudml.org/doc/33897},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Hiraoka, Yasuaki
TI - Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 6
SP - 797
EP - 806
AB - 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.
LA - eng
KW - rigorous numerics; exponential dichotomy; homoclinic orbits; numerical examples; exponential dichotomy; homoclinic orbits; reversible dynamical systems; Melnikov functions; algorithm
UR - http://eudml.org/doc/33897
ER -

References

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