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Suppose M be the projective limit of weak symplectic Banach manifolds\{(M_i,\phi_{ij})\}_{i,j\in\mathbb N}, where M_i are modeled over reflexiveBanach space and \sigma is compatible with the inverse system(defined in thearticle). We associate to each point x\in M, a Fr\'{e}chet space H_x(defined insection 3). We prove that if H_x are locally constant, then with certainsmoothness and boundedness condition, there exists Darboux chart for the weaksymplectic structure.

Darboux chart on Projective limit of weak symplectic Banach manifold