Dresden 2014 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 40: Poster - Quantum Systems/ Stat. Phys./ Diffusive Process
DY 40.1: Poster
Donnerstag, 3. April 2014, 17:00–19:00, P3
Global structure of regular tori in a generic 4D symplectic map — Steffen Lange1,2, Martin Richter1,2, •Franziska Onken1, Arnd Bäcker1,2, and Roland Ketzmerick1,2 — 1Institut für Theoretische Physik, TechnischeUniversität Dresden, 01062 Dresden, Germany — 2Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
We progress towards an understanding of the phase-space structures of higher-dimensional systems similar to the well-known case of Hamiltonian systems with two degrees of freedom. Using 3d phase-space slices and frequency analysis we investigate the global organization of regular tori of a generic 4d symplectic map with a mixed phase space. We visualize how all of the 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: The first type are Lyapunov families attached to elliptic-elliptic periodic orbits. These families are observed to exist even far away from their periodic orbit and beyond major resonance gaps. We explain how the second type originates from rank-1 resonances. At resonance gaps of both families either (i) periodic orbits exist, similiar to the Poincaré-Birkhoff theorem for 2d maps, or (ii) the family forms large bends. In combination these results allow for describing the self-similiar hierarchy of regular tori in the 4d phase space.