Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2003-02-13
Nonlinear Sciences
Exactly Solvable and Integrable Systems
LaTeX, 18 pages, 4 figures
Scientific paper
10.1088/1367-2630/5/1/367
The renormalization group method is applied to the study of discrete dynamical systems. As a particular example, the Henon map is considered as applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring possessing a FODO-cell structure with a single thin sextupole. A powerful renormalization group method is developed that is valid correct to fourth order in the perturbation amplitude, and a technique for resolving the resonance structure of the Henon map is also presented. This calculation represents the first successful application of a renormalization group method to the study of discrete dynamical system in a unified manner capable of reducing the dynamics of the system both far from and close to resonances, thus preserving the symplectic symmetry of the original map.
Davidson Ronald C.
Tzenov Stephan I.
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