Astronomy and Astrophysics – Astrophysics
Scientific paper
Oct 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996a%26a...314..795s&link_type=abstract
Astronomy and Astrophysics, v.314, p.795-806
Astronomy and Astrophysics
Astrophysics
7
Galaxies: Kinematics And Dynamics, Chaotic Phenomena, Celestial Mechanics
Scientific paper
The properties of orbits in spherically-symmetric systems oscillating with Miller and Smith's "second radial mode" are examined, in particular using spectra of stretching numbers (or spectra of short-time Lyapunov exponents, short time being of the order of the integration timestep). The spectra for regular orbits are symmetric, reflecting the symmetry of the trajectory in phase space; those for chaotic orbits are asymmetric. All the details of the spectra can be explained analytically in the time-independent case. The spectra of ordered orbits in the time-dependent case are similar. On the other hand, the spectra of chaotic orbits are invariant with respect to initial conditions in the same chaotic domain, while they are different for separated chaotic domains. In this case the difference spectrum, which is the antisymmetric part of the spectrum, is a sensitive tool for distinguishing orbits from different chaotic regions, more so than the Lyapunov characteristic number.
Contopoulos George
Smith Harlan J.
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