Rapid fluctuations of chaotic maps on RN
Huang, Yu Chen, Goong Ma, Daowei
Huang, Yu
Chen, Goong
Ma, Daowei
Citations
Altmetric:
Authors
Other Names
Location
Time Period
Advisors
Original Date
Digitization Date
Issue Date
2006-11-01
Type
Article
Genre
Keywords
Chaos,Dynamical systems,Fractals,Hausdorff dimensions,Total variations
Subjects (LCSH)
Citation
Yu Huang, Goong Chen, Daowei Ma, Rapid fluctuations of chaotic maps on RN, Journal of Mathematical Analysis and Applications, Volume 323, Issue 1, 2006, Pages 228-252, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2005.10.019.
Abstract
The iterates fn of a chaotic map f display heightened oscillations (or fluctuations) as n → ∞. If f is a chaotic interval map in one dimension, then it is now known that the total variation of fn on that interval grows exponentially with respect to n [G. Chen, T. Huang, Y. Huang, Chaotic behavior of interval maps and total variations of iterates, Internat. J. Bifur. Chaos 14 (2004) 2161-2186]. However, the characterization of chaotic behavior of maps in multi-dimensional spaces is generally much more challenging. Here, we generalize the definition of bounded variations for vector-valued maps in terms of the Hausdorff measure and then use it to study what we call rapid fluctuations on fractal sets in multi-dimensional chaotic discrete dynamical systems. The relations among rapid fluctuations, strict turbulence and positive entropy are established for Lipschitz continuous systems on general N-dimensional Euclidean spaces. Applications to planar monotone or competitive systems, and triangular systems on the square are also given. © 2005 Elsevier Inc. All rights reserved.
Table of Contents
Description
This is an open access article under the CC BY license.
Publisher
Academic Press Inc.
Journal
Journal of Mathematical Analysis and Applications
Book Title
Series
Digital Collection
Finding Aid URL
Use and Reproduction
Archival Collection
PubMed ID
ISSN
10960813