Lyapunov analysis of stable chaos in self-gravitating many body systems

Abstract

Elliptical galaxies seem to have two inconsistent characters in their dynamical structures: triaxial velocity dispersions of the stars suggest that the elliptical galaxies consist of regular stellar orbits, whereas nonlinear interaction in self-gravitating many-body systems makes the elliptical galaxies chaotic. A new type of chaos, “stable chaos”, in which orbits do not change significantly although they have orbital instability (positive Lyapunov exponent), is expected to give the key to clarify the dynamical structure of elliptical galaxies. As a first step, we examine whether the stable chaos appears or not in one-dimensional self-gravitating mass sheet systems.