 |  |  |
(1)
|
 |  |  |
(2)
|
where 
,
are computed mod 1 (Kaplan and Yorke
1979). The Kaplan-Yorke map with 
has correlation
exponent 
(Grassberger and Procaccia 1983) and capacity dimension
1.43 (Russell et al. 1980).
Kaplan-Yorke Map
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References
Grassberger, P. and Procaccia, I. "Measuring the Strangeness of Strange Attractors." Physica D 9, 189-208, 1983.Kaplan, J. L. and Yorke, J. A. In Functional Differential Equations and Approximations of Fixed Points: Proceedings, Bonn, July 1978 (Ed. H.-O. Peitgen and H.-O. Walther). Berlin: Springer-Verlag, p. 204, 1979.Russell, D. A.; Hanson, J. D.; and Ott, E. "Dimension of Strange Attractors." Phys. Rev. Let. 45, 1175-1178, 1980.Referenced on Wolfram|Alpha
Kaplan-Yorke MapCite this as:
Weisstein, Eric W. "Kaplan-Yorke Map." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kaplan-YorkeMap.html