R Szalai and H M Osinga 2008 Nonlinearity 21 273 doi:10.1088/0951-7715/21/2/004
Unstable manifolds of a limit cycle near grazing
R Szalai and H M Osinga
Show affiliationsRecommended by Y G Kevrekidis
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 it Lipschitz continuous, so that 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.
- PACS
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05.45.-a Nonlinear dynamics and nonlinear dynamical systems
- MSC
- Subjects
- Dates
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Issue 2 (February 2008)
Received 13 April 2007, in final form 16 December 2007
Published 21 January 2008
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Unstable manifolds of a limit cycle near grazing
R Szalai and H M Osinga 2008 Nonlinearity 21 273
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