Linear stability of symplectic maps

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Abstract
A general method is presented for analytically calculating linear stability limits for symplectic maps of arbitrary dimension in terms of the coefficients of the characteristic polynomial and the Krein signatures. Explicit results are given for dimensions 4, 6, and 8. The codimension and unfolding are calculated for all cases having a double eigenvalue on the unit circle. The results are applicable to many physical problems, including the restricted three‐body problem and orbital stability in particle accelerators.