  We summarize recent developments in the use of spectral methods for analyzing
large numbers of orbits in N-body simulations to obtain insights into the
global phase space structure of dark matter halos. The fundamental frequencies
of oscillation of orbits can be used to understand the physical mechanism by
which the shapes of dark matter halos evolve in response to the growth of
central baryonic components. Halos change shape primarily because individual
orbits change their shapes adiabatically in response to the growth of a
baryonic component, with those at small radii become preferentially rounder.
Chaotic scattering of orbits occurs only when the central point mass is very
compact and is equally effective for centrophobic long-axis tube orbits as it
is for centrophilic box orbits.
