  We suggest that polar rings and/or counter-rotating disks in flattened
galaxies can be formed from stars captured at the Binney resonance, where the
rate of precession of the angular momentum vector of a disk star equals the
pattern speed of a triaxial halo. If the halo pattern speed is initially
retrograde and slowly decays to zero, stars can be trapped as the Binney
resonance sweeps past them, and levitated into polar orbits. If the halo
pattern speed is initially retrograde and slowly changes to prograde, trapped
stars can evolve from prograde to retrograde disk orbits. The stellar
components of polar rings formed by this process should consist of two equal,
counter-rotating star streams.
