  This paper summarises an investigation of chaos in a toy potential which
mimics much of the behaviour observed for the more realistic triaxial
generalisations of the Dehnen potentials, which have been used to model cuspy
triaxial galaxies both with and without a supermassive black hole. The
potential is the sum of an anisotropic harmonic oscillator potential,
  V_o=(1/2)*(a^{2}x^{2}+b^{2}y^{2}+c^{2}z^{2}), and a spherical Plummer
potential,
  V_o=-M_{BH}/(r^{2}+e^{2})^{1/2} with r^{2}=x^{2}+y^{2}+z^{2}. Attention
focuses on three issues related to the properties of ensembles of chaotic
orbits which impact on chaotic mixing and the possibility of constructing
self-consistent equilibria: (1) What fraction of the orbits are chaotic? (2)
How sensitive are the chaotic orbits, i.e., how large are their largest (short
time) Lyapunov exponents? (3) To what extent is the motion of chaotic orbits
impeded by Arnold webs, i.e.,, how `sticky' are the chaotic orbits? These
questions are explored as functions of the axis ratio a:b:c, black hole mass
M_BH, softening length e, and energy E with the aims of understanding how the
manifestations of chaos depend on the shape of the system and why the black
hole generates chaos. The simplicity of the model makes it amenable to a
perturbative analysis. That it mimics the behaviour of more complicated
potentials suggests that much of this behaviour should be generic.
