## 抄録

The large deviation properties of the Lempel-Ziv complexity are studied using a one-dimensional non-hyperbolic chaos map called the "modified Bernoulli map", where the transition between stationary and non-stationary chaos is clearly observed. The upper limit of the Lempel-Ziv complexity in the non-stationary regime is theoretically evaluated, and the relationship between the algorithmic complexity and the Lempel-Ziv complexity is discussed. Non-stationary processes are universal phenomena in non-hyperbolic systems, and they are usually characterized by an infinite ergodic measure and intrinsic long time tails, such as 1/f^{ν} spectral fluctuations. It is shown that the Lempel-Ziv complexity obeys universal scaling laws and that the Lempel-Ziv complexity has the L^{1}-function property, which guarantees the Darling-Kac-Aaronson theorem for an infinite ergodic system. The most striking result is that the maximum diversity appears at the transition point from stationary chaos to non-stationary chaos where the exact 1/ f spectral process is generated.

本文言語 | English |
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ページ（範囲） | 503-515 |

ページ数 | 13 |

ジャーナル | Progress of Theoretical Physics |

巻 | 116 |

号 | 3 |

DOI | |

出版ステータス | Published - 2006 9 |

## ASJC Scopus subject areas

- Physics and Astronomy(all)