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

Access to Document

10.1016/0375-9601(88)90539-7

Cite this

@article{ce3c7595554a41068331ce4dfeca2cdf,

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.",

year = "1988",

month = dec,

day = "12",

doi = "10.1016/0375-9601(88)90539-7",

language = "English",

volume = "134",

pages = "19--24",

number = "1",

}

TY - JOUR

T1 - Vlasov equation on a symplectic leaf

AU - David Crawford, John

AU - Hislop, Peter D.

N1 - 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.

PY - 1988/12/12

Y1 - 1988/12/12

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.

UR - https://www.scopus.com/pages/publications/45449123168

UR - https://www.scopus.com/inward/citedby.url?scp=45449123168&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(88)90539-7

DO - 10.1016/0375-9601(88)90539-7

M3 - Article

AN - SCOPUS:45449123168

SN - 0375-9601

VL - 134

SP - 19

EP - 24

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1

ER -

Vlasov equation on a symplectic leaf

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this