THE MECHANISM OF THE INCREASE OF THE GENERALIZED DIMENSION OF A FILTERED CHAOTIC TIME-SERIES

被引：9

作者：

CHENNAOUI, A

LIEBLER, J

SCHUSTER, HG

机构：

[1] CHRISTIAN ALBRECHTS UNIV KIEL,INST THEORET PHYS,W-2300 KIEL 1,GERMANY

[2] UNIV KIEL STERNWARTE,W-2300 KIEL 1,GERMANY

来源：

JOURNAL OF STATISTICAL PHYSICS | 1990年 / 59卷 / 5-6期

关键词：

filtered time series of one-dimensional maps; Frobenius-Perron integral equation; generalized dimension D[!sub]q[!/sub; Hausdorff dimension; Liapunov exponent;

D O I：

10.1007/BF01334753

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The determination of the attractor dimension from an experimental time series may be affected by the influence of filters which are incorporated into many measuring processes. While this is expected from the Kaplan-Yorke conjecture, we show that for one-dimensional maps a weak filter can induce a self-similarity which is responsible for the increase of the Hausdorff dimension. We are able to calculate the increase of the generalized dimension Dq for the filtered time series of the logistic map xi+1=rxi(1-xi) at r=4 analytically. © 1990 Plenum Publishing Corporation.

引用

页码：1311 / 1328

页数：18

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