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- W2000112830 abstract "In this paper a Hamiltonian analogue of the well-known meandering transition from rotating waves to modulated rotating and modulated traveling waves in systems with the Euclidean symmetry of the plane is presented. In non-Hamiltonian systems, for example, in spiral wave dynamics, this transition is a Hopf bifurcation in a corotating frame, as external parameters are varied, and modulated traveling waves occur only at certain resonances. In Hamiltonian systems, for example, in systems of point vortices in the plane, the conserved quantities of the system, angular and linear momentum, are natural bifurcation parameters. Depending on the symmetry properties of the momentum map, either modulated traveling waves do not occur, or, in contrast to the dissipative case, modulated traveling waves are the typical scenario near rotating waves, as momentum is varied. Systems with the symmetry group of a sphere and with the Euclidean symmetry group of three-dimensional space are also treated." @default.
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- W2000112830 date "2008-01-01" @default.
- W2000112830 modified "2023-10-17" @default.
- W2000112830 title "A Hamiltonian Analogue of the Meandering Transition" @default.
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- W2000112830 doi "https://doi.org/10.1137/070704940" @default.
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