It is somewhat surprising, because one of the most famous papers in chaos theory, "The Applicability of the Third Integral of Motion" (Henon & Heiles), basicall

It is somewhat surprising, because one of the most famous papers in chaos theory, "The Applicability of the Third Integral of Motion" (Henon & Heiles), basically starts by saying a similar assumption isn't true, that stars aren't ergodically distributed in the axial/radial directions. If you have five equations of motion in a six-dimensional universe (3 space + 3 velocity coordinates), you can compute the future trajectory of each point. Two equations come from constant energy & angular momentum, and these constrain where in phase-space the trajectories can go. Another two equations are do not make any such constraints, which implies stars are at least ergodically distributed in a 2D phase-space. Since none of these equations constrain the axial/radial velocity, you would expect the dispersions to be equal for both directions. However, this turns out to not be the case. This means there must be a third isolating equation of motion out there, and the surprising thing Henon & Heiles find is it's chaotic! Sometimes it constrains points to 2D regions of phase-space (i.e. concentric circles of orbits), and other times it lets them move in a 3D region (i.e. chaotic trajectories filling the space).