Local coordinates (p,q) with ω=Σ dpᵢ∧dqᵢ. Moser trick. No local invariants.
graph TD
D1["Def: Darboux coords\nω = Σ dpᵢ∧dqᵢ"]
D2["Def: Moser trick\nω_t interp, find φ"]
D3["Def: Symplectic neighbor\nDarboux in nbhd"]
T1["Thm: Darboux\nlocally ω standard"]
T2["Thm: Moser\nω₀,ω₁ same vol⇒diffeo"]
T3["Thm: Weinstein\nLagrangian nbhd"]
T4["Thm: No local inv\nunlike Riemannian"]
T5["Thm: Gromov non-squeeze\nball→cylinder"]
D1 --> T1
D2 --> T2
D3 --> T1
T1 --> T4
T2 --> T3
T4 --> T5
classDef definition fill:#b197fc,color:#fff
classDef theorem fill:#51cf66,color:#fff
class D1,D2,D3 definition
class T1,T2,T3,T4,T5 theorem
Process Statistics
- Nodes: 13
- Edges: 10
Frontier: math.SG