Let D be an open disk in R² and consider the open subset D×R^(n-1)×R^(n-1) of R^(2n) with the standard symplectic structure. Also let l_(0), l₁be two open arcs in D which are closed as subsets of D meeting each other transversely at exactly two points.
We construct a Hamiltonian flow with compact support, Ψ_(u) : D×R^(n-1)×R^(n-1)→D×R^(n-1)×R^(n-1), 0 ≤ u ≤ 1 such that Ψ_(0) = 1 and . Ψ₁(l_(0)×R^(n-1)×0)∩(l₁×0×R^(n-1)) = φ.
Construction of such Ψ_(u), 0 ≤ u ≤ 1, deserves called a Lagrangian Whitney trick. We will show that the condition is needed involving the areas of the regions D in divided by l_(0) and l₁for the construction.