  Classical periodic orbits responsible for emergence of the superdeformed
shell structures for single-particle motions in spheroidal cavities are
identified and their relative contributions to the shell structures are
evaluated. Both prolate and oblate superdeformations (axis ratio about 2:1) as
well as prolate hyperdeformation (axis ratio about 3:1) are investigated.
Fourier transforms of quantum spectra clearly show that three-dimensional
periodic orbits born out of bifurcations of planar orbits in the equatorial
plane become predominant at large prolate deformations, while butterfly-shaped
planar orbits bifurcated from linear orbits along the minor axis are important
at large oblate deformations.
