Chains of rotational tori and filamentary structures close to high multiplicity periodic orbits in a 3D galactic potential

Abstract

This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use the method of color and rotation [Patsis and Zachilas 1994] in order to visualize them. As examples we use the case of two orbits, one 2-periodic and one 7-periodic. We investigate the structure of multiple tori around them in the 4D surface of section and in addition we study the orbital behavior in the neighborhood of the corresponding simple unstable periodic orbits. By considering initially a few consequents in the neighborhood of the orbits in both cases we find a structure in the space of section, which is in direct correspondence with what is observed in a resonance zone of a 2D autonomous Hamiltonian system. However, in our 3D case we have instead of stability islands rotational tori, while the chaotic zone connecting the points of the unstable periodic orbit is replaced by filaments extending in 4D following a smooth color variation. For more intersections, the consequents of the orbit which started in the neighborhood of the unstable periodic orbit, diffuse in phase space and form a cloud that occupies a large volume surrounding the region containing the rotational tori. In this cloud the colors of the points are mixed. The same structures have been observed in the neighborhood of all m-periodic orbits we have examined in the system. This indicates a generic behavior.

12 pages,22 figures, Accepted for publication in the International Journal of Bifurcation and Chaos

References in corpus (1)

• The structure of invariant tori in a 3D galactic potential

Cited by in corpus (9)

• The phase-space of boxy-peanut and X-shaped bulges in galaxies I. Properties of non-periodic orbits
• Chaos and dynamical trends in barred galaxies: bridging the gap between N-body simulations and time-dependent analytical models
• The dynamics of a spinning particle in a linear in spin Hamiltonian approximation
• The orbital content of bars: The origin of 'non-x1-tree', bar-supporting orbits
• Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model
• The structure of phase space close to fixed points in a 4D symplectic map
• Visualizing the Phase Space of the HeI_2 van der Waals Complex using Lagrangian Descriptors
• Partially chaotic orbits in a perturbed cubic force model
• The Phase Space Structure in the vicinity of vertical Lyapunov orbits around L1,2 in a barred galaxy model