Homoclinic orbits of invertible maps

J. M. Bergamin, T. Bountis, M. N. Vrahatis

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

In this paper, we present a systematic method for finding all homoclinic orbits of invertible maps in any finite dimension. One advantage of this method is that it can also be used to order and classify all the homoclinic orbits, using symbolic dynamics, if a certain criterion is satisfied. We also present a more direct scheme, which quickly locates homoclinic orbits without, however, being able to order and classify them. Our work represents an extension of a method introduced in an earlier paper, with which one could only find homoclinic orbits possessing a certain symmetry. Thus, asymmetric homoclinic orbits can now be as easily computed. One application of our results is the explicit construction of breather (and multibreather) solutions of a class of one-dimensional nonlinear lattices.

Original languageEnglish
Pages (from-to)1603-1619
Number of pages17
JournalNonlinearity
Volume15
Issue number5
DOIs
Publication statusPublished - Sep 2002
Externally publishedYes

Fingerprint

Homoclinic Orbit
Invertible
Orbits
orbits
Classify
Nonlinear Lattice
Breathers
Symbolic Dynamics
Symmetry
symmetry

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Bergamin, J. M., Bountis, T., & Vrahatis, M. N. (2002). Homoclinic orbits of invertible maps. Nonlinearity, 15(5), 1603-1619. https://doi.org/10.1088/0951-7715/15/5/313

Homoclinic orbits of invertible maps. / Bergamin, J. M.; Bountis, T.; Vrahatis, M. N.

In: Nonlinearity, Vol. 15, No. 5, 09.2002, p. 1603-1619.

Research output: Contribution to journalArticle

Bergamin, JM, Bountis, T & Vrahatis, MN 2002, 'Homoclinic orbits of invertible maps', Nonlinearity, vol. 15, no. 5, pp. 1603-1619. https://doi.org/10.1088/0951-7715/15/5/313
Bergamin JM, Bountis T, Vrahatis MN. Homoclinic orbits of invertible maps. Nonlinearity. 2002 Sep;15(5):1603-1619. https://doi.org/10.1088/0951-7715/15/5/313
Bergamin, J. M. ; Bountis, T. ; Vrahatis, M. N. / Homoclinic orbits of invertible maps. In: Nonlinearity. 2002 ; Vol. 15, No. 5. pp. 1603-1619.
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