ABSTRACT
Alex Dragt has continued to explore how one could improve the computation of approximate Taylor maps emphasizing longitudinal accuracy instead of transverse accuracy. The local part is based on kick codes and the global part is based on normal forms: approximate maps must be coming from the tracking code if they are to be trusted. The need for a new paradigm, a new theoretical framework based on the common metaphors of the field, is not derived from the success of approximate maps as tracking engines. It is however derived from tracking, that is to say from our relative ability to produce reliable phase plots using "kick codes" and the relative inability to analyze precisely the equations of motion which produced these plots. More important John Irwin has applied map/Lie methods to the design and understanding of final focusing systems.
