# On the generalization of the Darboux theorem

## TL;DR

This paper establishes conditions under which Darboux charts exist on weakly symplectic bounded Fréchet manifolds, extending the classical Darboux theorem to an infinite-dimensional setting using Moser's trick.

## Contribution

It introduces sufficient conditions for Darboux charts on weakly symplectic bounded Fréchet manifolds, advancing the understanding of symplectic geometry in infinite dimensions.

## Key findings

- Darboux charts exist under specified conditions on weakly symplectic bounded Fréchet manifolds.
- Application of Moser's trick in an infinite-dimensional context.
- Extension of classical Darboux theorem to Fréchet manifolds.

## Abstract

We provide sufficient conditions for the existence of Darboux charts on weakly symplectic bounded Fr\'{e}chet manifolds by using the Moser's trick.