### 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.

Original language | English |
---|---|

Pages (from-to) | 284-290 |

Number of pages | 7 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 53 |

Issue number | 1 SUPPL. A |

Publication status | Published - 1996 |

Externally published | Yes |

## Fingerprint Dive into the research topics of 'Evolution of the Liouville density of a chaotic system'. Together they form a unique fingerprint.

## Cite this

Peres, A., & Terno, D. (1996). Evolution of the Liouville density of a chaotic system.

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,*53*(1 SUPPL. A), 284-290.