More generally, one can add a Hamiltonian term in the Cauchy-Riemann equation, and replace transverse intersection points by Hamiltonian chords. The Cauchy-Riemann equation then gets modified to the Floer equation

$$\partial_{s}u+J(t,u)(\partial_{t}u-X_{H})=0,$$

(65)

where $X_{H}$ is a Hamiltonian vector field. This perturbation is not needed for Floer theoretic transversality statements if $L$ and $L^{\prime}$ are already transverse, but is an essential ingredient in showing the Hamiltonian invariance of Floer cohomology.