Vlasov equation on a symplectic leaf

John David Crawford, Peter D. Hislop

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageEnglish
Pages (from-to)19-24
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number1
StatePublished - 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.

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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