  Resolved surveys of the Milky Way's stellar halo can obtain all 6 phase space
coordinates of tens of thousands of individual stars, making it possible to
compute their 3-dimensional orbits. Spectral analysis of large numbers of halo
orbits can be used to construct frequency maps which are a compact, yet
informative representation of their phase space distribution function (DF).
Such maps can be used to infer the major types of orbit families that
constitute the DF of stellar halo and their relative abundances. The structure
of the frequency maps, especially the resonant orbits, reflects the formation
history and shape of the dark matter potential and its orientation relative to
the disk. The application of frequency analysis to cosmological hydrodynamic
simulations of disk galaxies shows that the orbital families occupied by halo
stars and dark matter particles are very similar, implying that stellar halo
orbits can be used to constrain the DF of the dark matter halo, possibly
impacting future direct dark matter detection experiments. An application of
these methods to a sample of \sim 16,000 Milky Way halo and thick disk stars
from the SDSS-SEGUE survey yields a frequency map with strong evidence for
resonant trapping of halo stars by the Milky Way disk, in a manner predicted by
controlled simulations in which the disk grows adiabatically. The application
of frequency analysis methods to current and future phase space data for Milky
Way halo stars will provide new insights into the formation history of the
dierent components of the Galaxy and the DF of the halo.
