Normal form theory for relative equilibria and relative periodic solutions |
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| Authors: | Jeroen S W Lamb Ian Melbourne |
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| Institution: | Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom ; Department of Mathematics and Statistics, University of Surrey, Guildford GU2 7XH, United Kingdom |
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| Abstract: | We show that in the neighbourhood of relative equilibria and relative periodic solutions, coordinates can be chosen so that the equations of motion, in normal form, admit certain additional equivariance conditions up to arbitrarily high order. In particular, normal forms for relative periodic solutions effectively reduce to normal forms for relative equilibria, enabling the calculation of the drift of solutions bifurcating from relative periodic solutions. |
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