On one-dimensional cohomology of the Lie algebra of divergence-free vector fields and on rotation numbers of dynamic systems

  • Vladimir I. Arnold
Part of the Vladimir I. Arnold - Collected Works book series (ARNOLD, volume 2)


§ 1. Definitions. Let A be a Lie algebra. A commutant [A, A] is a set of finite sums of the commutators of elements A. The group of one-dimensional cohomologies H1(A, R) is the linear space dual to A/[A, A].


Volume Element Poisson Bracket Symplectic Manifold Rotation Number Hamilton Function 
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Copyright information

© Russ. Acad. Sciences 1969

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
  1. 1.HeidelbergGermany

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