The Zaslavskii map is a discrete-time dynamical system introduced by

George M. Zaslavsky George M. Zaslavsky (Cyrillic: Георгий Моисеевич Заславский) (31 May 1935 – 25 November 2008) was a Soviet mathematical physicist and one of the founders of the physics of dynamical chaos.chaotic behavior. The Zaslavskii map takes a point (

x_n,y_n

) in the

plane Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * Planes (gen ...

and maps it to a new point: :

, (\textrm\,1)

y_=e^(y_n+\epsilon\cos(2\pi x_n))\,

and :

\mu = \frac

where ''mod'' is the

modulo operator In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is th ...

with real arguments. The map depends on four constants ''ν'', ''μ'', ''ε'' and ''r''. Russel (1980) gives a Hausdorff dimension of 1.39 but Grassberger (1983) questions this value based on their difficulties measuring the correlation dimension.

References

*
(LINK)
*
(LINK)
*
(LINK)
{{Chaos theory Chaotic maps

See also

References