  Dynamic stabilization of atomic hydrogen against ionization in high-frequency
single- and two-color, circularly polarized laser pulses is observed by
numerically solving the three-dimensional, time-dependent Schr\"odinger
equation. The single-color case is revisited and numerically determined
ionization rates are compared with both, exact and approximate high-frequency
Floquet rates. The position of the peaks in the photoelectron spectra can be
explained with the help of dressed initial states. In two-color laser fields of
opposite circular polarization the stabilized probability density may be shaped
in various ways. For laser frequencies $\omega_1$ and $\omega_2=n\omega_1$,
$n=2,3,...$ and sufficiently large excursion amplitudes $n+1$ distinct
probability density peaks are observed. This may be viewed as the
generalization of the well-known ``dichotomy'' in linearly polarized laser
fields, i.e, as ``trichotomy,'' ``quatrochotomy,'' ``pentachotomy'' etc. All
those observed structures and their ``hula-hoop''-like dynamics can be
understood with the help of high-frequency Floquet theory and the two-color
Kramers-Henneberger transformation. The shaping of the probability density in
the stabilization regime can be realized without additional loss in the
survival probability, as compared to the corresponding single-color results.
