Arnold cat map

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The Arnold Cat map is an area-preserving map on the two-dimensional torus defined by

\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} \mod 1 \;.

It was introduced by Vladimir Arnold and he used a sketch of a cat to illustrate the chaotic properties of this map. It is an example of an Anosov diffeomorphism.


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References

Arnold, V. I. and A. Avez (1968). Ergodic Problems of Classical Mechanics. New York, Benjamin.

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See Also

Dynamical Systems, Mapping, Anosov Diffeomorphism

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