This article is cited in 1 paper

On the Linearization of Hamiltonian Systems on Poisson Manifolds

Yu. M. Vorob'ev<sup>ab

a</sup> Moscow State Institute of Electronics and Mathematics
^b University of Sonora

Abstract: The linearization of a Hamiltonian system on a Poisson manifold at a given (singular) symplectic leaf gives a dynamical system on the normal bundle of the leaf, which is called the first variation system. We show that the first variation system admits a compatible Hamiltonian structure if there exists a transversal to the leaf which is invariant with respect to the flow of the original system. In the case where the transverse Lie algebra of the symplectic leaf is semisimple, this condition is also necessary.

UDC: 517

Received: 28.09.2004

DOI: 10.4213/mzm2601

 English version: Mathematical Notes, 2005, 78:3, 297–303

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