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A Hamiltonian Analogue of the Meandering Transition

Wulff, C (2008) A Hamiltonian Analogue of the Meandering Transition SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 7 (4). 1213 - 1246. ISSN 1536-0040

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Abstract

In this pap er 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 p oint vortices in the plane, the conserved quantities of the system, angular and linear momentum, are natural bifurcation parameters. Dep ending on the symmetry prop erties 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.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Physical Sciences, Mathematics, Applied, Physics, Mathematical, Mathematics, Physics, meandering transition, resonance drift, symmetric Hamiltonian systems, RELATIVE PERIODIC-ORBITS, POINT VORTICES, MOMENTUM MAPS, SPIRAL WAVES, EQUILIBRIA, DYNAMICS, BIFURCATIONS, PERSISTENCE, SYMMETRY, SYSTEMS
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:42
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1536

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