THE SPECTRUM OF CHAOTIC TIME SERIES (I): FOURIER ANALYSIS

被引：7

作者：

Chen, Goong ^{[1
,4
]}

Hsu, Sze-Bi ^{[2
]}

Huang, Yu ^{[3
]}

Roque-Sol, Marco A. ^{[4
]}

机构：

[1] Texas A&M Univ Qatar, Sci Program, Doha, Qatar

[2] Natl Tsing Hua Univ, Dept Math, Hsinchu 300, Taiwan

[3] Sun Yat Sen Zhongshan Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

[4] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2011年 / 21卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Li-Yorke chaos; topological entropy; total variation; Sobolev spaces; Fourier coefficients; EXCITATION BOUNDARY-CONDITION; DIMENSIONAL WAVE-EQUATION; ENTROPY; DEFINITION; VIBRATIONS; MAPS;

D O I：

10.1142/S0218127411029136

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The question of spectral analysis for deterministic chaos is not well understood in the literature. In this paper, using iterates of chaotic interval maps as time series, we analyze the mathematical properties of the Fourier series of these iterates. The key idea is the connection between the total variation and the topological entropy of the iterates of the interval map, from where special properties of the Fourier coefficients are obtained. Various examples are given to illustrate the applications of the main theorems.

引用

页码：1439 / 1456

页数：18

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