Chaotic Diffusion in a Triaxial Galactic Model: An Example of Global Stable Chaos

Abstract

In this work we focus on the chaotic diffusion in the phase space of a triaxial potentialresembling an elliptical galaxy. The transport process is studied in two different action-likestarting spaces in order to cope with circulating and noncirculating orbits. Estimates of thediffusion rate obtained by means of the variance approach are discussed in detail and theirlimitations are exposed. After revisiting the Shannon-entropy-based method from a conceptualpoint of view in the framework of simple arguments taken from the information theory, we applyit to measure changes in the unperturbed actions or integrals of motion of the system for differentsets of small ensembles of random initial conditions. For such sets of ensembles, estimates of theLyapunov times are also provided. The results show that, within the chaotic component of thephase space, the Lyapunov times are shorter than any physical time scale as the Hubble time,but the diffusion times are much larger than the latter. Thus, we conclude that stable chaosdominates the dynamics of realistic galactic models.