Arnold cat map - davidar/scholarpedia GitHub Wiki

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

<math>

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

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

Dynamical Systems, Mapping, Anosov Diffeomorphism

Category:Dynamical Systems Category:Mappings