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In their example, the two Lagrangians are given by the diagonal of $W\times W$ and a graph of Hamiltonian. How does it generalize to arbitrary (transversal) pair of Lagrangians in $W$? Also, in their definition of Hamiltonian Floer, their equation is $u_s+J_tu_t$ and requires only $u(s,t+1)=f(u(s,t))$, instead of $u_s+Ju_t+JX_t$ with $u(s,t+1)=u(s,t)$. Are they equivalent?