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Unstable manifolds of a limit cycle near grazing

Research output: Working paperWorking paper and Preprints

Original languageEnglish
StatePublished - 2007


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.

Additional information

Additional information: Submitted to the journal Nonlinearity

Research areas

  • global manifold, grazing bifurcation

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  • Preprint

    Submitted manuscript, 254 KB, PDF-document


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