Re: "Determinant" as a Hamiltonian


when n is even,R^(n^2) has a symplectic structure,so my question is well defined!

IMO, this does not make any sense. To call a
function "a
Hamiltonian", you need to have a symplectic (or
Poisson) structure.
Without it, your function is "just a quadratic
function", which are
"all the same" (in general position).

Hope this helps,
Ilya


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