The harmonic structure of generic Kerr orbits
  Generic Kerr orbits exhibit intricate three-dimensional motion. We offer a
classification scheme for these intricate orbits in terms of periodic orbits.
The crucial insight is that for a given effective angular momentum $L$ and
angle of inclination $\iota$, there exists a discrete set of orbits that are
geometrically $n$-leaf clovers in a precessing {\it orbital plane}. When viewed
in the full three dimensions, these orbits are periodic in $r-\theta$. Each
$n$-leaf clover is associated with a rational number,
$1+q_{r\theta}=\omega_\theta/\omega_r$, that measures the degree of perihelion
precession in the precessing orbital plane. The rational number $q_{r\theta}$
varies monotonically with the orbital energy and with the orbital eccentricity.
Since any bound orbit can be approximated as near one of these periodic
$n$-leaf clovers, this special set offers a skeleton that illuminates the
structure of all bound Kerr orbits, in or out of the equatorial plane.
