Berlin 2015 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 55: Poster - Quantum Systems
DY 55.2: Poster
Thursday, March 19, 2015, 16:00–18:00, Poster A
Global structure of regular tori in a generic 4D symplectic map — •Steffen Lange1, Franziska Onken1, Arnd Bäcker1,2, and Roland Ketzmerick1,2 — 1TU Dresden, Institut für Theoretische Physik, Dresden — 2MPI für Physik komplexer Systeme, Dresden
The dynamics of Hamiltonian systems (e.g., planetary motion) can be investigated by symplectic maps. While the phase-space structures of 2d symplectic maps are well established, much less is known for higher dimensions.
Using 3d phase-space slices[1] and frequency analysis we investigate the global organization of regular tori of a generic 4d symplectic map with a mixed phase space[2]. We show how all of the regular 2d-tori are organized around a skeleton of elliptic 1d-tori in the 4d phase space. The 1d-tori occur in two types of one-parameter families: The first type are Lyapunov families attached to elliptic-elliptic periodic orbits. We explain how the second type originates from remnants of broken resonant 2d-tori. In combination these results allow for describing the self-similar hierarchy of regular tori in the 4d phase space analogous to the island-around-island hierarchy in 2d maps.
[1] M. Richter, S. Lange, A. Bäcker, and R. Ketzmerick, Visualization and comparison of classical structures and quantum states of four-dimensional maps, Phys. Rev. E 89, 022902 (2014)
[2] S. Lange, M. Richter, F. Onken, A. Bäcker and R. Ketzmerick, Global structure of regular tori in a generic 4D symplectic map, Chaos 24, 024409 (2014)