EVOLUTION OF THE LIOUVILLE DENSITY OF A CHAOTIC SYSTEM

An area-preserving map of the unit sphere, consisting of alternating t wists 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 functi ons. As the dynamical mapping proceeds, it is found that the number of non-negligible coefficients increases exponentially with the number o f steps. This is in contrast to the behavior of a Schrodinger wave fun ction, which requires, for the analogous quantum system, a basis of fi xed size.