In this talk I will revisit the concept of N-body chaos in the continuum
limit of self-gravitating systems described by the collisionless
Boltzmann-Poisson equations. In particular, with the aid of N-body
simulations I will question the use of frozen N-body realizations to obtain
qualitative information on the N-body chaos in particle systems with large
N. Moreover, I will present some recent results concerning the so-called
Radial-orbit instability (ROI) that rule out N-body chaos as a source of
such process relevant for the dynamical evolution of elliptical galaxies.
Finally, I will discuss the effects of externally imposed noise and
friction on the onset of ROI.
The results presented here do not apply only to the case of
self-gravitating systems but can be extended also to other long-range
interacting systems such as for example non-neutral plasmas and charged
particle beams.