Unstable manifolds of a limit cycle near grazing

R Szalai, HM Osinga

Research output: Working paper

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We study the local dynamics of an impacting system near a grazing bifurcation point. In particular, we investigate local invariant manifolds of grazing periodic orbits. At a grazing bifurcation point the local return map does not have a Jacobian nor is of Lipschitz continuous, so that the classical theory does not apply. Nevertheless, we are able to use the Graph Transform technique and show that under certain conditions a local Lipschitz unstable manifold of the periodic orbit exists at the grazing bifurcation point.
Original languageEnglish
Publication statusPublished - 2007

Bibliographical note

Additional information: Submitted to the journal Nonlinearity

Structured keywords

  • Engineering Mathematics Research Group


  • global manifold
  • grazing bifurcation


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