A note on the geometry of linear Hamiltonian systems of signature 0 in R⁴
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dimensionshamiltonianlagrangianlinearnumberplanessignatureaccording
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It is shown that a linear Hamiltonian system of signature zero in 4 dimensions is elliptic or hyperbolic according to the number of Lagrangian planes in the null-cone $H^{-1}(0)$, or equivalently the number of invariant Lagrangian planes. An extension to higher dimensions is described.
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