# Arnold Cat Map

From Scholarpedia

(Redirected from Cat map)

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.

## References

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