Arnold cat map

From Scholarpedia
(Redirected from Arnold's cat map)
Jump to: navigation, search

    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.

    See Also

    Dynamical Systems, Mapping, Anosov Diffeomorphism

    Personal tools
    Namespaces

    Variants
    Actions
    Navigation
    Focal areas
    Activity
    Tools