Hamiltonian structures of the first variation equations and symplectic connections

Yu. M. Vorob'ev

Sbornik. Mathematics, Tome 191 (2000) no. 4, pp. 477-502

Résumé

Necessary and sufficient conditions in terms of symplectic connections, ensuring that the first variation equation of a Hamiltonian system along a fixed invariant symplectic submanifold is also a Hamiltonian system with respect to some admissible symplectic structure are obtained. The class of admissible symplectic structures is distinguished by means of the natural condition of compatibility with the symplectic 2-form in the ambient space. Possible obstructions to the existence of a Hamiltonian structure on the first variation equation are investigated.

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