Please use this identifier to cite or link to this item:
http://hdl.handle.net/1983/917
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| Title: | Unstable manifolds of a limit cycle near grazing |
| Author(s): | Szalai, R
Osinga, HM |
| Publication or creation date: | 2007 |
| Abstract: | 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. |
| Subject keywords: | global manifold
grazing bifurcation |
| Additional information: | Submitted to the journal Nonlinearity |
| Document type: | Preprint |
| Appears in Collections: | Bristol Centre for Applied Nonlinear Mathematics
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