Split Lagrangian tori in non-monotone S^2 × S^2 are Hamiltonian isotopic exactly when their base points lie on the same good billiard trajectory in a rectangle.
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Lagrangian split tori in $S^2 \times S^2$ and billiards
Split Lagrangian tori in non-monotone S^2 × S^2 are Hamiltonian isotopic exactly when their base points lie on the same good billiard trajectory in a rectangle.