The how of a fluid in a rapidly rotating spherical shell whose rotation rat
e is modulated sinusoidally in time is simulated numerically. Different ine
rtial modes are excited as the modulation frequency is varied. The inertial
modes are structured by internal layers. Internal layers are reflected at
the boundaries such that at certain modulation frequencies, the layers are
focused onto "attractors" after multiple reflections. The geometric propert
ies of these attractors and their relevance for the response of the fluid i
s investigated. [S1063-651X(99)06402-8].