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Frequency map analysis [J. Laskar, Icarus 88, 266 (1990)] is used here to analyze the transverse dynamics of four third generation synchrotron light sources: the ALS, the ESRF, the SOLEIL project, and Super-ACO. Time variations of the betatron tunes give additional information for the global dynamics of the beam. The main resonances are revealed; a one-to-one correspondence between the configuration space and the frequency space can be performed. We stress that the frequency maps, and therefore the dynamics optimization, are highly sensitive to sextupolar strengths and vary in a large amount from one machine to another. The frequency maps can thus be used to characterize the different machines

Review of single particle dynamics for third generation light sources through frequency map analysis