# Kaplan–Yorke map

The **Kaplan–Yorke map** is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior. The Kaplan–Yorke map takes a point (*x _{n}, y_{n} *) in the plane and maps it to a new point given by

where *mod* is the modulo operator with real arguments. The map depends on only the one constant α.

## Calculation method

Due to roundoff error, successive applications of the modulo operator will yield zero after some ten or twenty iterations when implemented as a floating point operation on a computer. It is better to implement the following equivalent algorithm:

where the and are computational integers. It is also best to choose to be a large prime number in order to get many different values of .

## References

- J.L. Kaplan and J.A. Yorke (1979). H.O. Peitgen and H.O. Walther, ed.
*Functional Differential Equations and Approximations of Fixed Points (Lecture notes in Mathematics 730)*. Springer-Verlag. ISBN 0-387-09518-7. - P. Grassberger and I. Procaccia (1983). "Measuring the strangeness of strange attractors".
*Physica*.**9D**(1-2): 189–208. Bibcode:1983PhyD....9..189G. doi:10.1016/0167-2789(83)90298-1.

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