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Assume that we have one of the 4 types of generating functions (say F(p, Q)) which defines a symplectomorphism $T$: $(P,Q) = (u(p,q), v(p,q))$. Now we can make a substitution and get a function $G(p,q)...

In the book Introduction to symplectic topology by MC Duff and Salamon, a discrete analogue of the action functional is defined on $\mathbb{R}^{2n}$. The idea is that a Hamiltonian isotopy can be ...