THE SPECTRUM OF CHAOTIC TIME SERIES (I): FOURIER ANALYSIS-Reference-Cited by-同舟云学术

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

Published:2011-05 Issue:05 Volume:21 Page:1439-1456
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

CHEN GOONG¹²,HSU SZE-BI³,HUANG YU⁴,ROQUE-SOL MARCO A.¹

Affiliation:

1. Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA

2. Science Program, Texas A&M University at Qatar Doha, Qatar

3. Department of Mathematics, National Tsing Hua University, No. 101, Sec. 2, Guangfu Rd., Hsinchu, Taiwan 300, R.O.C.

4. Department of Mathematics, Sun Yat-sen (Zhongshan) University, No. 135 Xingang Road West, Guangzhou 510275, P. R. China

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127411029136

Reference23 articles.

1. Topological entropy

2. On Devaney's Definition of Chaos

3. Dynamics in One Dimension

4. Entropy for group endomorphisms and homogeneous spaces

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