 9818 Bambusi, Dario
 On Darboux theorem for weak symplectic manifolds
(382K, PS)
Jan 14, 98

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Abstract. A new tool to study reducibility of a weak symplectic
form to a constant one is introduced and used to prove a version of
Darboux theorem more general than previous ones. More precisely, at each
point of the considered manifold a Banach space is associated to the
symplectic form (dual of the phase space with respect to the symplectic
form), and it is shown that Darboux theorem holds if such a space is
locally constant. The following application is given. Consider a weak
symplectic manifold $M$ on which Darboux theorem is assumed to hold
(e.g. a symplectic vector space). It is proved that Darboux theorem
holds also for any finite codimension symplectic submanifolds of $M$,
and for symplectic manifolds obtained from $M$ by MarsdenWeinstein
reduction procedure.
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