Symplectic maps
نویسنده
چکیده
Here Dfij = ∂fi/∂zj is the Jacobian matrix of f , J is the Poisson matrix, and I is the n × n identity matrix. Equivalently, Stokes’ theorem can be used to show that the loop action, A[γ] = ∮ γ pdq, is preserved by f for any contractible loop γ on X. If f preserves the loop action for all loops, even those that are not contractible, then it is exact symplectic. When n = 1, the symplectic condition is equivalent to det(Df) = 1, so that the map is area– and orientation–preserving. Examples include the
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