Zaslavskii Map

The 2-D map

$$x_{n+1} = [x_n+\nu(1+\mu y_n)+\epsilon\nu\mu\cos(2\pi x_n)]\quad ({\rm mod\ }1)$$

$$y_{n+1} = e^{-\Gamma}[y_n+\epsilon\cos(2\pi x_n)],$$

where

$$\mu\equiv {1-e^{-\Gamma}\over\Gamma}$$

(Zaslavskii 1978). It has Correlation Exponent $\nu\approx 1.5$ (Grassberger and Procaccia 1983) and Capacity Dimension 1.39 (Russell et al. 1980).

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.