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.