Evolution of the Liouville density of a chaotic system

Asher Peres*, Daniel Terno

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)284-290
Number of pages7
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number1 SUPPL. A
Publication statusPublished - 1996
Externally publishedYes


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