  This talk provides a progress report on an extended collaboration which has
aimed to address two basic questions, namely: Should one expect to see cuspy,
triaxial galaxies in nature? And can one construct realistic cuspy, triaxial
equilibrium models that are robust? Three technical results are described: (1)
Unperturbed chaotic orbits in cuspy triaxial potentials can be extraordinarily
sticky, much more so than orbits in many other three-dimensional potentials.
(2) Even very weak perturbations can be important by drastically reducing,
albeit not completely eliminating, this stickiness. (3) A simple toy model
facilitates a simple understanding of why black holes and cusps can serve as an
effective source of chaos. These results suggest that, when constructing models
of galaxies using Schwarzschild's method or any analogue thereof, astronomers
would be well advised to use orbital building blocks that have been perturbed
by `noise' or other weak irregularities, since such building blocks are likely
to be more nearly time-independent than orbits evolved in the absence of all
perturbations.
