Darboux chart on Projective limit of weak symplectic Banach manifold

الأصل · EN

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mᵢ,ϕij)}i,j, where Mᵢ are modeled over reflexive Banach space and σis compatible with the inverse system(defined in the article). We associate to each point x∈ M, a Fréchet space Hₓ(defined in section 3). We prove that if Hₓ are locally constant, then with certain smoothness and boundedness condition, there exists Darboux chart for the weak symplectic structure.