It is shown how the methods can be extended to also allow a rigorous treatment of the Lagrange remainder term of the Taylor expansion. The methods can be applied for the estimation of the effects going beyond the aberration order; it is also for the study of the repetitive motion where, leaning on ideas of Lyapunov, Nekhoroshev and others, it for the first time allows a rigorous determination of guaranteed particle survival times.
M. Berz, K. Makino, Proc. SPIE Charged Particle Optics III 3155 (1997) 186-192
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