  I argue that the widely adopted framework of stellar dynamics survived since
1940s, is not fitting the current knowledge on non-linear systems. Borrowed
from plasma physics when several fundamental features of perturbed non-linear
systems were unknown, that framework ignores the difference in the role of
perturbations in two different classes of systems, in plasma with Debye
screening and gravitating systems with no screening. Now, when the
revolutionary role of chaotic effects is revealed even in planetary dynamics
i.e. for nearly integrable systems, one would expect that for stellar systems,
i.e. non-integrable systems, their role have to be far more crucial. Indeed,
ergodic theory tools already enabled to prove that spherical stellar systems
are exponentially instable due to N-body interactions, while the two-body
encounters, contrary to existing belief, are not the dominating mechanism of
their relaxation. Chaotic effects distinguish morphological and other
properties of galaxies. Using the Ricci curvature criterion, one can also show
that a central massive object (nucleus) makes the N-body gravitating system
more instable (chaotic), while systems with double nuclei are even more
instable than those with a single one.
