remark 24.13 What Darboux's theorem forbids

Rests on

• depends_on corollary A.69 No local invariants ¶
  • depends_on theorem A.68 Darboux ¶
    • depends_on definition A.67 Symplectic manifold ¶
      • depends_on definition 13.105 Closed form ¶
        • depends_on definition 13.103 Exterior derivative ¶
        • depends_on definition 13.98 $k$-form ¶
      • depends_on definition 13.98 $k$-form ¶ ↺
      • depends_on definition 13.48 Differentiable manifold ¶
        • depends_on definition 13.47 Differentiable structure ¶
    • depends_on equation 5.144 eq:lin-symplectic-normal-form ¶
    • depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
      • depends_on definition 5.110 Bilinear map ¶
        • depends_on definition 5.37 Linear transformation ¶
      • depends_on definition 5.113 Non-degenerate form ¶
        • depends_on definition 5.110 Bilinear map ¶ ↺
      • depends_on definition 5.111 Symmetric and antisymmetric forms ¶
        • depends_on definition 5.110 Bilinear map ¶ ↺
        • depends_on equation 5.137 eq:lin-bilinear-matrix ¶
      • depends_on equation 5.139 eq:lin-bilinear-congruence ¶
      • proves proof ch:03-linear-algebra-representations@proof-54 ¶
    • proves proof app:A-long-proofs@proof-57 ¶
  • proves proof app:A-long-proofs@proof-50 ¶
• depends_on theorem 24.12 Darboux ¶
  • depends_on definition 24.8 Symplectic manifold ¶
    • depends_on definition 13.105 Closed form ¶ ↺
    • depends_on definition 13.98 $k$-form ¶ ↺
    • depends_on definition 24.2 Symplectic vector space ¶
      • depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶ ↺
  • depends_on theorem A.68 Darboux ¶ ↺
  • proves proof ch:07-symplectic-geometry@prooflink-1 ¶

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