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. https://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 |
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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: | https://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: | 03 Oct 2019 02:02 |
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