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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Normal form theory for relative equilibria and relative periodic solutions


Authors: Jeroen S. W. Lamb and Ian Melbourne
Journal: Trans. Amer. Math. Soc. 359 (2007), 4537-4556
MSC (2000): Primary 37G40, 37G05, 37G15, 37C55
DOI: https://doi.org/10.1090/S0002-9947-07-04314-0
Published electronically: April 17, 2007
MathSciNet review: 2309197
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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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Additional Information

Jeroen S. W. Lamb
Affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
Email: jeroen.lamb@imperial.ac.uk

Ian Melbourne
Affiliation: Department of Mathematics and Statistics, University of Surrey, Guildford GU2 7XH, United Kingdom
Email: ism@math.uh.edu

DOI: https://doi.org/10.1090/S0002-9947-07-04314-0
Received by editor(s): November 15, 2005
Published electronically: April 17, 2007
Additional Notes: The first author would like to thank the UK Engineering and Physical Sciences Research Council (EPSRC), the Nuffield Foundation and the UK Royal Society for support during the course of this research.
The first and second authors would like to thank IMPA (Rio de Janeiro) for hospitality during a visit in which part of this work was done.
Article copyright: © Copyright 2007 American Mathematical Society