Lagrange intersections in a symplectic space (Q5930973)

The Clifford torus is a Lagrangian torus in the symplectic four-space which is a product of two circles which have the same radii, lie in the transversal symplectic two-dimensional subspaces and are centered at the origin. The author proves that for any linear symplectic automorphism of the four-space such a torus and its image always intersect and generically have eight points of intersection. The author also proves some higj-dimensional generalizations of this theorem.