SPECTRA OF STRETCHING NUMBERS OF ORBITS IN OSCILLATING GALAXIES

The properties of orbits in spherically-symmetric systems oscillating with Miller and Smith's ''second radial mode'' are examined, in partic ular using spectra of stretching numbers (or spectra of short-time Lya punov exponents, short time being of the order of the integration time step). The spectra for regular orbits are symmetric, reflecting the sy mmetry of the trajectory in phase space; those for chaotic orbits are asymmetric. All the details of the spectra can be explained analytical ly in the time-independent case. The spectra of ordered orbits in the time-dependent case are similar. On the other hand, the spectra of cha otic orbits are invariant with respect to initial conditions in the sa me chaotic domain, while they are different for separated chaotic doma ins. In this case the difference spectrum, which is the antisymmetric part of the spectrum, is a sensitive tool for distinguishing orbits fr om different chaotic regions, more so than the Lyapunov characteristic number.