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 language | English |
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Publication status | Published - 2007 |
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Additional information: Submitted to the journal Nonlinearity
- Engineering Mathematics Research Group
- global manifold
- grazing bifurcation