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[[File:Zaslavskii map.png|thumb|right|'''Zaslavskii map''' with parameters: <math>\epsilon=5, \nu=0.2, r=2.</math>]]
The '''Zaslavskii map''' is a [[discrete-time]] [[dynamical system]] introduced by [[George M. Zaslavsky]].   It is an example of a dynamical system that exhibits [[chaos theory  | chaotic behavior]].  The Zaslavskii map takes a point (<math>x_n,y_n</math>) in the [[plane (mathematics)|plane]] and [[function (mathematics)|maps]] it to a new point:
 
:<math>x_{n+1}=[x_n+\nu(1+\mu y_n)+\epsilon\nu\mu\cos(2\pi x_n)]\, (\textrm{mod}\,1)</math>
:<math>y_{n+1}=e^{-r}(y_n+\epsilon\cos(2\pi x_n))\,</math>
 
and
:<math>\mu = \frac{1-e^{-r}}{r}</math>
 
where ''mod'' is the [[modulo operation|modulo operator]] with real arguments. The map depends on four [[Constant (mathematics)|constant]]s ''&nu;'', ''&mu;'', ''&epsilon;'' and ''r''. Russel (1980) gives a [[Hausdorff dimension]] of 1.39 but [[Peter Grassberger | Grassberger]] (1983) questions this value based on their difficulties measuring the [[correlation dimension]].
 
==See also==
* [[List of chaotic maps]]
 
==References==
* {{cite journal | author=G.M. Zaslavskii | title=The Simplest case of a strange attractor | journal=Phys. Lett. A | year=1978 | volume=69 |issue=3| pages=145–147 | doi=10.1016/0375-9601(78)90195-0|bibcode = 1978PhLA...69..145Z }} [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)]
* {{cite journal | author=D.A. Russel, J.D. Hanson, and E. Ott | title=Dimension of strange attractors | journal=Phys. Rev. | year=1980 | volume=45 | issue=14 | pages=1175 | doi=10.1103/PhysRevLett.45.1175 | bibcode=1980PhRvL..45.1175R}} [http://prola.aps.org/abstract/PRL/v45/i14/p1175_1 (LINK)]
* {{cite journal | author=[[Peter Grassberger | P. Grassberger]] and I. Procaccia | title=Measuring the strangeness of strange attractors | journal=Physica | year=1983 | volume=9D| pages=189–208 | doi=10.1016/0167-2789(83)90298-1 | bibcode=1983PhyD....9..189G}} [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1983PhyD....9..189G&amp;db_key=PHY  (LINK)]
 
{{Chaos theory}}
 
[[Category:Chaotic maps]]
 
{{Mathapplied-stub}}

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