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Vlasov moment flows and geodesics on the Jacobi group

Gay-Balmaz, F and Tronci, C (2011) Vlasov moment flows and geodesics on the Jacobi group arXiv.

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Abstract

By using the moment algebra of the Vlasov kinetic equation, we characterize the integrable Bloch-Iserles system on symmetric matrices (arXiv:math-ph/0512093) as a geodesic flow on the Jacobi group. We analyze the corresponding Lie-Poisson structure by presenting a momentum map, which both untangles the bracket structure and produces particle-type solutions that are inherited from the Vlasov-like interpretation. Moreover, we show how the Vlasov moments associated to Bloch-Iserles dynamics correspond to particular subgroup inclusions into a group central extension (first discovered in arXiv:math/0410100), which in turn underlies Vlasov kinetic theory. In the most general case of Bloch-Iserles dynamics, a generalization of the Jacobi group also emerges naturally.

Item Type: Article
Authors :
NameEmailORCID
Gay-Balmaz, FUNSPECIFIEDUNSPECIFIED
Tronci, Cc.tronci@surrey.ac.ukUNSPECIFIED
Date : 9 May 2011
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:21
Last Modified : 17 May 2017 15:03
URI: http://epubs.surrey.ac.uk/id/eprint/834967

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