Global structure of regular tori in a generic 4D symplectic map Artikel uri icon

Open Access

  • false

Peer Reviewed

  • true

Abstract

  • Chaos 24, 024409 (2014) For the case of generic 4D 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 3D
    phase-space slice. This visualizes how all regular 2-tori are organized around
    a skeleton of elliptic 1-tori in the 4D phase space. The 1-tori occur in two
    types of one-parameter families: (a) Lyapunov families emanating from
    elliptic-elliptic periodic orbits, which are observed to exist even far away
    from them and beyond major resonance gaps, and (b) families originating from
    rank-1 resonances. At resonance gaps of both types of families either (i)
    periodic orbits exist, similar to the Poincare-Birkhoff theorem for 2D maps, or
    (ii) the family may form large bends. In combination these results allow for
    describing the hierarchical structure of regular tori in the 4D phase space
    analogously to the islands-around-islands hierarchy in 2D maps.

Veröffentlichungszeitpunkt

  • November 6, 2014