On one-dimensional cohomology of the Lie algebra of divergence-free vector fields and on rotation numbers of dynamic systems
§ 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].
KeywordsVolume Element Poisson Bracket Symplectic Manifold Rotation Number Hamilton Function
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