SEMICLASSICS OF ROTATION AND TORSION

We discuss semiclassical approximations of the spectrum of the periodi cally kicked top, both by diagonalizing the semiclassically approximat ed Floquet matrix F and by employing periodic-orbit theory. In the reg ular case when F accounts only for a linear rotation periodic-orbit th eory yields the exact spectrum. In the chaotic case the first method y ields the quasienergies with an accuracy of better than 3% of the mean spacing. By working in the representation where the torsional part of the Floquet matrix is diagonal our semiclassical work is mostly an ap plication of the asymptotics of the rotation matrix, i. e. of Wigner's so-called d-functions.