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

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

Abstract

§ 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].

Keywords

Volume Element Poisson Bracket Symplectic Manifold Rotation Number Hamilton Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Russ. Acad. Sciences 1969

Authors and Affiliations

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

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