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The renormalization group method is applied to the study of discretedynamical systems. As a particular example, the Henon map is considered asapplied to describe the transverse betatron oscillations in a cyclicaccelerator or storage ring possessing a FODO-cell structure with a single thinsextupole. A powerful renormalization group method is developed that is validcorrect to fourth order in the perturbation amplitude, and a technique forresolving the resonance structure of the Henon map is also presented. Thiscalculation represents the first successful application of a renormalizationgroup method to the study of discrete dynamical system in a unified mannercapable of reducing the dynamics of the system both far from and close toresonances, thus preserving the symplectic symmetry of the original map.Comment: LaTeX, 18 pages, 4 figure

Renormalization group reduction of the Hénon map and application to the transverse betatron motion in cyclic accelerators