The Zaslavskii map is a discrete-time dynamical system introduced by George M. Zaslavsky. It is an example of a dynamical system that exhibits chaotic behavior. The Zaslavskii map takes a point (${\displaystyle x_{n},y_{n}}$) in the plane and maps it to a new point:

${\displaystyle x_{n+1}=[x_{n}+\nu (1+\mu y_{n})+\epsilon \nu \mu \cos(2\pi x_{n})]\,({\textrm {mod}}\,1)}$

${\displaystyle y_{n+1}=e^{-r}(y_{n}+\epsilon \cos(2\pi x_{n}))\,}$

and

${\displaystyle \mu ={\frac {1-e^{-r}}{r}}}$

where mod is the modulo operator 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.