Math @ Duke

Publications [#318307] of Ding Ma
Papers Published
 Huang, Y; Chen, G; Ma, D, Rapid fluctuations of chaotic maps on R^{N},
Journal of Mathematical Analysis and Applications, vol. 323 no. 1
(November, 2006),
pp. 228252 [doi]
(last updated on 2017/12/17)
Abstract: The iterates f n 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 f n 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) 21612186]. However, the characterization of chaotic behavior of maps in multidimensional spaces is generally much more challenging. Here, we generalize the definition of bounded variations for vectorvalued maps in terms of the Hausdorff measure and then use it to study what we call rapid fluctuations on fractal sets in multidimensional chaotic discrete dynamical systems. The relations among rapid fluctuations, strict turbulence and positive entropy are established for Lipschitz continuous systems on general Ndimensional Euclidean spaces. Applications to planar monotone or competitive systems, and triangular systems on the square are also given. © 2005 Elsevier Inc. All rights reserved.


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