Zaslavskii map

The Zaslavskii map is a discrete-time dynamical system. 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:

:$x\_\{n+1\}=\; [x\_n+\; u(1+mu\; y\_n)+epsilon\; umucos(2pi\; x\_n)]\; ,\; (\; extrm\{mod\},1)$:$y\_\{n+1\}=e^\{-r\}(y\_n+epsiloncos(2pi\; x\_n)),$

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

* [http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TVM-46S32M9-11N-1&_cdi=5538&_user=10&_orig=browse&_coverDate=12%2F11%2F1978&_sk=999309996&view=c&wchp=dGLbVtb-zSkWA&md5=381ecc59b5847c0a67dbe457cae92c46&ie=/sdarticle.pdf (LINK)]
* [http://prola.aps.org/abstract/PRL/v45/i14/p1175_1 (LINK)]
* [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1983PhyD....9..189G&db_key=PHY (LINK)]

ee also

* List of chaotic maps