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Global structure of regular tori in a generic 4D symplectic map
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/content/aip/journal/chaos/24/2/10.1063/1.4882163
2014-06-11
2014-08-22

Abstract

For the case of generic 4 symplectic maps with a mixed phase space, we investigate the global organization of regular tori. For this, we compute elliptic 1-tori of two coupled standard maps and display them in a 3 phase-space slice. This visualizes how all regular 2-tori are organized around a skeleton of elliptic 1-tori in the 4 phase space. The 1-tori occur in two types of one-parameter families: (α) Lyapunov families emanating from elliptic-elliptic periodic orbits, which are observed to exist even far away from them and beyond major resonance gaps, and (β) families originating from rank-1 resonances. At resonance gaps of both types of families either (i) periodic orbits exist, similar to the Poincaré-Birkhoff theorem for 2 maps, or (ii) the family may form large bends. In combination, these results allow for describing the hierarchical structure of regular tori in the 4 phase space analogously to the islands-around-islands hierarchy in 2 maps.

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Scitation: Global structure of regular tori in a generic 4D symplectic map
http://aip.metastore.ingenta.com/content/aip/journal/chaos/24/2/10.1063/1.4882163
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