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Manuscript Title: A program to compute Birkhoff normal forms of symplectic maps in R**4. | ||

Authors: A. Bazzani, M. Giovannozzi, E. Todesco | ||

Program title: ARES | ||

Catalogue identifier: ADAO_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 86(1995)199 | ||

Programming language: Fortran. | ||

Computer: ALPHAVAX 3000/500. | ||

Operating system: VMS, UNIX. | ||

RAM: 1.2M words | ||

Peripherals: disc. | ||

Keywords: Particle physics, Elementary, Accelerator, Symplectic maps, Birkhoff normal forms, Resonances. | ||

Classification: 11.10. | ||

Nature of problem:The computation of normal forms of symplectic maps provides informations on the structure of the phase space in a neighbourhood of a fixed point. This approach can be useful in beam dynamics to analyse the effects of nonlinearities of a magnetic lattice. The normal forms allow one to analytically optimize a magnetic lattice, constructing effective correction strategies for the multipolar errors. | ||

Solution method:The computation of normal forms is based on the solution of a conjugation equation for the initial map. It is convenient to represent both the normalizing transformation and the normal form by means of a Lie transformation. Then we can solve the equation by a perturbative method on the homogeneous orders of the Taylor expansion. The main algorithmic tool is the composition of two polynomial maps up to a given order in the Taylor expansion. | ||

Running time:17.7 sec. on ALPHAVAX 3000/500 or 19.5 sec. on HP 755 at perturbative order 10 in the quasi-resonant case. |

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