Zaslavskii map - Alchetron, The Free Social Encyclopedia

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 ( x n , y n ) in the plane and maps it to a new point:

x n + 1 = [ x n + ν ( 1 + μ y n ) + ϵ ν μ cos ⁡ ( 2 π x n ) ] ( mod 1 ) y n + 1 = e − r ( y n + ϵ cos ⁡ ( 2 π x n ) )

and

μ = 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.

References

Zaslavskii map Wikipedia

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