A non-transverse homoclinic orbit to a saddle-node equilibrium

AR Champneys, Jorg Haerterich, B Sandstede

Research output: Working paper

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A homoclinic orbit is considered for which the center-stable and center-unstable manifolds of a saddle-node equilibrium have a quadratic tangency. This bifurcation is of codimension two and leads generically to the creation of a bifurcation curve defining two independent transverse homoclinic orbits to a saddle-node. This latter case was shown by Shilnikov to imply shift dynamics. It is proved here that in a large open parameter region of the codimension-two singularity, the dynamics are completely described by a perturbation of the Henon-map giving strange attractors, Newhouse sinks and the creation of the shift dynamics. In addition, an example system admitting this bifurcation is constructed and numerical computations are performed on it
Original languageEnglish
Publication statusPublished - 1994

Bibliographical note

Additional information: Preprint of a paper later published by the Cambridge University Press, (1996) Ergodic Theory and Dynamical Systems 16 (3), pp. 431-450. ISSN 0143-3857

Terms of use: © Cambridge University Press 1996

Structured keywords

  • Engineering Mathematics Research Group


  • shift dynamics
  • homoclinic orbit
  • manifold
  • codimension two
  • saddle-node equilibrium
  • bifurcation


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