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Poisson structure and invariant manifolds on Lie groups

Marsden, Jerrold E. and Pekarsky, Sergey and Shkoller, Steve (2000) Poisson structure and invariant manifolds on Lie groups. In: EQUADIFF 99. World Scientific , Singapore , pp. 1192-1197. ISBN 9789810243593 http://resolver.caltech.edu/CaltechAUTHORS:20100908-084300019

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Abstract

For a discrete mechanical system on a Lie group G determined by a (reduced) Lagrangian ℓ we define a Poisson structure via the pull-back of the Lie-Poisson structure on g^∗ by the corresponding Legendre transform. The main result shown in this paper is that this structure coincides with the reduction under the symmetry group G of the canonical discrete Lagrange 2-form ω_L on G × G. Its symplectic leaves then become dynamically invariant manifolds for the reduced discrete system.


Item Type:Book Section
Additional Information:© World Scientific, 2000. The authors would like to thank Alan Weinstein for pointing out the connections with the general theory of dynamics on groupoids and algebroids.
Record Number:CaltechAUTHORS:20100908-084300019
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100908-084300019
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19820
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:15 Sep 2010 21:21
Last Modified:26 Dec 2012 12:24

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