Kaplan-Yorke Map

$\displaystyle x_{n+1}$	$\textstyle =$	$\displaystyle 2x_n$
$\displaystyle y_{n+1}$	$\textstyle =$	$\displaystyle \alpha y_n+\cos(4\pi x_n),$

where

are computed mod 1. (Kaplan and Yorke 1979). The Kaplan-Yorke map with $\alpha=0.2$ has Correlation Exponent $1.42\pm 0.02$ (Grassberger Procaccia 1983) and Capacity Dimension 1.43 (Russell et al. 1980).

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 (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.