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The Equivariant Darboux Theorem

* Exploiting Symmetry in Applied and Numerical Analysis *
(E. Allgower et al eds.) 1992 AMS-SIAM Summer Seminar Proceedings.
Lectures in Appl. Math. **29** (1993) 163-169

** Michael Dellnitz and Ian Melbourne **

** Abstract **

The classical Darboux Theorem states that symplectic
forms are locally constant up to isomorphism, or equivalently that any
two symplectic forms are locally isomorphic. We consider the
corresponding results for symplectic forms that are invariant under the
action of a compact Lie group. In this context, it is still true that
symplectic forms are locally constant up to isomorphism but it is not
true that any two symplectic forms are locally isomorphic.

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