Evolution of the Liouville density of a chaotic system
- 1 January 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 53 (1) , 284-290
- https://doi.org/10.1103/physreve.53.284
Abstract
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. © 1996 The American Physical Society.Keywords
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