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Abstract

This survey article reviews the theory and application of homoclinic orbits to equilibria in reversible continuous-time dynamical systems, where the homoclinic orbit and the equilibrium are both reversible. The focus is on even-order reversible systems in four or more dimensions. Local theory, generic argument, and global existence theories are examined for each qualitatively distinct linearisation. Several recent results, such as coalescence caused by non-transversality and the reversible orbit-flip bifurcation are covered. A number of open problems are highlighted. Applications are reviewed to systems arising from a variety of disciplines. With the aid of numerical methods, three examples are presented in detail, one of which is infinitely dimensional
Original languageEnglish
DOIs
Publication statusPublished - Aug 1997

Bibliographical note

Additional information: Submitted to Elsevier Preprint, December 1996. Revised version July 1997. Later published by Elsevier Science, (1998) Physica D: Nonlinear Phenomena, 112 (1-2), pp. 158-186. ISSN 0167-2789

Keywords

  • global existence theory
  • generic argument theory
  • homoclinic orbits
  • survey article
  • reversible orbit-flip bifurcation
  • local theory, generic argument, and global existence theories
  • coalescence caused by non-transversality
  • even-order reversible continuous-time dynamical systems in four or more dimensions

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