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Mat. Zametki, 2005, Volume 78, Issue 3, Pages 323–330 (Mi mz2601)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Linearization of Hamiltonian Systems on Poisson Manifolds

Yu. M. Vorob'evab

a 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.

DOI: https://doi.org/10.4213/mzm2601

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

Bibliographic databases:

UDC: 517
Received: 28.09.2004

Citation: Yu. M. Vorob'ev, “On the Linearization of Hamiltonian Systems on Poisson Manifolds”, Mat. Zametki, 78:3 (2005), 323–330; Math. Notes, 78:3 (2005), 297–303

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ruiz-Pantaleon J.C., Garcia-Beltran D., Vorobiev Yu., “Infinitesimal Poisson Algebras and Linearization of Hamiltonian Systems”, Ann. Glob. Anal. Geom., 58:4 (2020), 415–431  crossref  mathscinet  isi
  • Математические заметки Mathematical Notes
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