Abstract
We numerically investigate the projections of non periodic orbits in a 4-dimensional (4-D) symplectic map composed of two coupled 2-dimensional (2-D) maps. We describe in detail the structures that are produced in different planes of projection and we find how the morphology of the 4-D orbits is influenced by the features of the 2-D maps as the coupling parameter increases. We give an empirical law that describes this influence.
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References
Arnold V. I.: 1963, Russ. Math, Surv. 18, 5.
Bountis T, and Tompaidis S,: 1990, in W, Scandale and G, Turchetti (eds.), p, 112, Numerical Problems in Future Particle Accelerators.
Contopoulos G.: 1984, Physica 11D, 179.
Contopoulos G. and Giorgilli A.: 1988, Meccanica 23, 19.
Froeschlé C.: 1972, Astron. Astrophys. 16, 172.
Kolmogorov A. N.: 1954, Dokl. Akad. Nauk., SSSR 98, 527.
MacKay R. S., Meiss J. D. and Percival I. C.: 1984, Physica 13D, 55.
Moser J.: 1962, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl. 2, 1.
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Skokos, C., Contopoulos, G. & Polymilis, C. Structures in the phase space of a four dimensional symplectic map. Celestial Mech Dyn Astr 65, 223–251 (1996). https://doi.org/10.1007/BF00053508
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DOI: https://doi.org/10.1007/BF00053508