Computation of error effects in nonlinear Hamiltonian systems using Lie algebraic methods
Journal of Mathematical Physics, Volume 33, Issue 6, pp. 1948-1963
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There exist Lie algebraic methods for obtaining transfer maps around any given trajectory of a Hamiltonian system. This paper describes an iterative procedure for finding transfer maps around the same trajectory when the Hamiltonian is perturbed by small linear terms. Such terms often result when an actual system deviates from an ideal one due to errors. Two examples from accelerator physics are worked out. Comparisons with numerical computations, and in simple cases exact analytical calculations, demonstrate the validity of the procedure.
An improved and more general technique is described in Healy, Liam M.,Journal of Mathematical Physics, Vol. 42, pp. 698-712, "Computation of Lie transfer maps for perturbed Hamiltonian systems" (2001).