Normal form theory for relative equilibria and relative periodic solutions

Lamb, Jeroen; Melbourne, Ian

doi:10.1090/S0002-9947-07-04314-0

Normal form theory for relative equilibria and relative periodic solutions
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by Jeroen S. W. Lamb and Ian Melbourne PDF

Trans. Amer. Math. Soc. 359 (2007), 4537-4556 Request permission

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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