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The Hamiltonian-dissipative decomposition of normal forms of vector fields

Lewis, D. and Marsden, J. (1989) The Hamiltonian-dissipative decomposition of normal forms of vector fields. In: Proceedings of the Conference on Bifurcation and its Numerical Analysis. Xi'an Jiaotong Univ. Press , Xi'an, China, pp. 51-78. ISBN 7-5605-0257-1 http://resolver.caltech.edu/CaltechAUTHORS:20100823-080520574

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Abstract

We consider dynamical systems in two variables with nilpotent linearization at the origin. We show that the behavior of the equilibria of such systems is determined by a modified Hamiltonian function which is constructed from an appropriate normal form for the vector field. In particular, the equilibria of the dynamical system correspond to critical points of the modified Hamiltonian and the local behavior of the vector field near an equilibrium is determined by the second variation of the modified Hamiltonian and its time derivative.


Item Type:Book Section
Additional Information:© 1989. This paper was directly inspired by some comments of Marty Golubitsky. We also thank Dieter Armbruster, John Guckenheimer, Phil Holnies, Peter Olver, and Jan Sanders for helpful comments.
Record Number:CaltechAUTHORS:20100823-080520574
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100823-080520574
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19575
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:23 Aug 2010 20:57
Last Modified:26 Dec 2012 12:20

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