# Cat map like maps without period

Is there any area-preserving chaotic map other than Arnold cat map which can be applied on a rectangle as well as being reversible but not periodic?

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What do you mean by the term "not periodic" ? Do you mean it should have no periodic points ? If so, then it is not possible because a continuous map on a compact manifold (rectangle) will have atleast one fixed point (which is just a periodic point of period 1) by Brouwer's theorem. – nonlinearism Mar 14 '13 at 18:56

Sure. There are Cat maps other than Arnold's Cat map. One general form of 2D Cat map is $${\bf{C}} = \begin{bmatrix}1 & a \\b & ab+1\end{bmatrix}$$