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The unregularized gradient flow of the symplectic action. (English) Zbl 0633.53058

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 the trajectories of which 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.
Reviewer: A.Floer

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
37C10 Dynamics induced by flows and semiflows
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