Vlasov equation on a symplectic leaf

John David Crawford; Peter D. Hislop

doi:10.1016/0375-9601(88)90539-7

Vlasov equation on a symplectic leaf

John David Crawford, Peter D. Hislop

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The infinite dimensional phase space of the Vlasov equation is foliated by symplectic manifolds (leaves) which are invariant under the dynamics. By adopting a Lie transform representation, exp{W, }, for near-identity canonical transformations we obtain a local coordinate system on a leaf. The evolution equation defined by restricting the Vlasov equation to the leaf is approximately represented by the evolution of W. We derive the equation for ∂_tW and show that it is hamiltonian relative to the nondegenerate Kirillov-Kostant-Souriau symplectic structure.

Original language	English
Pages (from-to)	19-24
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	134
Issue number	1
DOIs	https://doi.org/10.1016/0375-9601(88)90539-7
State	Published - Dec 12 1988

Bibliographical note

Funding Information:
The first authorh ase njoyedu sefulc onversations with J. Marsdena nd P. Morrison. This work was supportedb y theA CM programo f DARPA, andt he DARPA University ResearchI nitiative Grant No. 00014-86-K-0758.

Funding

The first authorh ase njoyedu sefulc onversations with J. Marsdena nd P. Morrison. This work was supportedb y theA CM programo f DARPA, andt he DARPA University ResearchI nitiative Grant No. 00014-86-K-0758.

Funders	Funder number
DARPA University	00014-86-K-0758
Defense Advanced Research Projects Agency

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/0375-9601(88)90539-7

Cite this

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title = "Vlasov equation on a symplectic leaf",

abstract = "The infinite dimensional phase space of the Vlasov equation is foliated by symplectic manifolds (leaves) which are invariant under the dynamics. By adopting a Lie transform representation, exp{W, }, for near-identity canonical transformations we obtain a local coordinate system on a leaf. The evolution equation defined by restricting the Vlasov equation to the leaf is approximately represented by the evolution of W. We derive the equation for ∂tW and show that it is hamiltonian relative to the nondegenerate Kirillov-Kostant-Souriau symplectic structure.",

author = "{David Crawford}, John and Hislop, {Peter D.}",

note = "Funding Information: The first authorh ase njoyedu sefulc onversations with J. Marsdena nd P. Morrison. This work was supportedb y theA CM programo f DARPA, andt he DARPA University ResearchI nitiative Grant No. 00014-86-K-0758.",

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N2 - The infinite dimensional phase space of the Vlasov equation is foliated by symplectic manifolds (leaves) which are invariant under the dynamics. By adopting a Lie transform representation, exp{W, }, for near-identity canonical transformations we obtain a local coordinate system on a leaf. The evolution equation defined by restricting the Vlasov equation to the leaf is approximately represented by the evolution of W. We derive the equation for ∂tW and show that it is hamiltonian relative to the nondegenerate Kirillov-Kostant-Souriau symplectic structure.

AB - The infinite dimensional phase space of the Vlasov equation is foliated by symplectic manifolds (leaves) which are invariant under the dynamics. By adopting a Lie transform representation, exp{W, }, for near-identity canonical transformations we obtain a local coordinate system on a leaf. The evolution equation defined by restricting the Vlasov equation to the leaf is approximately represented by the evolution of W. We derive the equation for ∂tW and show that it is hamiltonian relative to the nondegenerate Kirillov-Kostant-Souriau symplectic structure.

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Vlasov equation on a symplectic leaf

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