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 o
rbits 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.
Stellar population studies show that low mass galaxies in all environments exhibit stellar halos that are older and more spherically distributed than the main body of the galaxy. In some cases, there is a significant intermediate age component that e
xtends beyond the young disk. We examine a suite of Smoothed Particle Hydrodynamic (SPH) simulations and find that elevated early star formation activity combined with supernova feedback can produce an extended stellar distribution that resembles these halos for model galaxies ranging from $v_{200}$ = 15 km s$^{-1}$ to 35 km s$^{-1}$, without the need for accretion of subhalos.
