# The unregularized gradient flow of the symplectic action

@article{Floer1988TheUG, title={The unregularized gradient flow of the symplectic action}, author={Andreas Floer}, journal={Communications on Pure and Applied Mathematics}, year={1988}, volume={41}, pages={775-813} }

The symplectic action can be defined on the space of smooth paths in a symplectic manifold P which join two Lagrangian submanifolds of P. To pursue a new approach to the variational theory of this function, we define on a subset of the path space the flow whose trajectories are given by the solutions of the Cauchy-Riemann equation with respect to a suitable almost complex structure on P. In particular, we prove compactness and transversality results for the set of bounded trajectories.

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