An area-preserving map of the unit sphere, consisting of alternating twists and turns, is mostly chaotic. A Liouville density on that sphere is specified by means of its expansion into spherical harmonics. That expansion initially necessitates only a finite number of basis functions. As the dynamical mapping proceeds, it is found that the number of non-negligible coefficients increases exponentially with the number of steps. This is in contrast to the behavior of a Schrödinger wave function, which requires, for the analogous quantum system, a basis of fixed size.
|Number of pages||7|
|Journal||Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Issue number||1 SUPPL. A|
|Publication status||Published - 1996|