Vlasov equation on a symplectic leaf |
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Institution: | 1. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;3. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China |
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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. |
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