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General Volume-Preserving Mechanical Systems

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Abstract

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold M, ω) via the highest Euler–Lagrange cohomology. It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in Hamilton mechanics. The ordinary canonical equations are included as a special case with a 2-form 1/(n - 1)Hω, where H is the corresponding Hamiltonian.

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Authors and Affiliations

  1. Institute of High Energy Physics, Chinese Academy of Sciences, PO Box 918-4, Beijing, 100039, P.R. China

    Bin Zhou

  2. Institute of Theoretical Physics, Chinese Academy of Sciences, PO Box 2735, Beijing, 100080, P.R. China

    Han-Ying Guo

  3. Department of Mathematics, Capital Normal University, Beijing, 100037, P.R. China

    Ke Wu

Authors
  1. Bin Zhou
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  2. Han-Ying Guo
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  3. Ke Wu
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Zhou, B., Guo, HY. & Wu, K. General Volume-Preserving Mechanical Systems. Letters in Mathematical Physics 64, 235–243 (2003). https://doi.org/10.1023/A:1025765428059

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