## 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 ∂_{t}W and show that it is hamiltonian relative to the nondegenerate Kirillov-Kostant-Souriau symplectic structure.

Original language | English |
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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 | |

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 |
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DARPA University | 00014-86-K-0758 |

Defense Advanced Research Projects Agency |

## ASJC Scopus subject areas

- General Physics and Astronomy