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Zaslavskii Map


The two-dimensional map

x_(n+1)=[x_n+nu(1+muy_n)+epsilonnumucos(2pix_n)] (mod 1)
(1)
y_(n+1)=e^(-Gamma)[y_n+epsiloncos(2pix_n)],
(2)

where

 mu=(1-e^(-Gamma))/Gamma
(3)

(Zaslavskii 1978). It has correlation exponent nu approx 1.5 (Grassberger and Procaccia 1983) and capacity dimension 1.39 (Russell et al. 1980).


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References

Grassberger, P. and Procaccia, I. "Measuring the Strangeness of Strange Attractors." Physica D 9, 189-208, 1983.Russell, D. A.; Hanson, J. D.; and Ott, E. "Dimension of Strange Attractors." Phys. Rev. Let. 45, 1175-1178, 1980.Zaslavskii, G. M. "The Simplest Case of a Strange Attractor." Phys. Let. 69A, 145-147, 1978.

Referenced on Wolfram|Alpha

Zaslavskii Map

Cite this as:

Weisstein, Eric W. "Zaslavskii Map." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ZaslavskiiMap.html

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