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

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. © 2011 World Scientific Publishing Company.

authors

• Chen, Goong

author list (cited authors)

• CHEN, G., HSU, S., HUANG, Y. U., & ROQUE-SOL, M. A.

citation count

• 6

publication date

• May 2011

publisher

• World Scientific Pub Co Pte Lt  Publisher

published in

• International Journal of Bifurcation and Chaos  Journal

keywords

• Fourier Coefficients
• Li-yorke Chaos
• Sobolev Spaces
• Topological Entropy
• Total Variation

Digital Object Identifier (DOI)

• 10.1142/s0218127411029136

start page

• 1439

end page

• 1456

volume

• 21

issue

• 05