Abstract
Persistence and bifurcations of Lyapunov manifolds can be studied by a combination of averaging-normalization and numerical bifurcation methods. This can be extended to infinite-dimensional cases when using suitable averaging theorems. The theory is applied to the case of a parametrically excited wave equation. We find fast dynamics in a finite, resonant part of the spectrum and slow dynamics elsewhere. The resonant part corresponds with an almost-invariant manifold and displays bifurcations into a wide variety of phenomena among which are 2- and 3-tori.
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Communicated by G. Haller.
T. Bakri is now at TNO Built Environment and Geosciences, P.O. Box 49, 2600 AA Delft, The Netherlands.
H.G.E. Meijer is now at Twente University, PO Box 217, 7500 AE Enschede, The Netherlands
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Bakri, T., Meijer, H.G.E. & Verhulst, F. Emergence and Bifurcations of Lyapunov Manifolds in Nonlinear Wave Equations. J Nonlinear Sci 19, 571–596 (2009). https://doi.org/10.1007/s00332-009-9045-2
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DOI: https://doi.org/10.1007/s00332-009-9045-2