The best known example of an Anosov Diffeomorphism. It is given by the Transformation

(1) 
where and are computed mod 1. The Arnold cat mapping is nonHamiltonian, nonanalytic, and mixing.
However, it is AreaPreserving since the Determinant is 1. The Lyapunov
Characteristic Exponents are given by

(2) 
so

(3) 
The Eigenvectors are found by plugging into the Matrix Equation

(4) 
For , the solution is

(5) 
where is the Golden Ratio, so the unstable (normalized) Eigenvector is

(6) 
Similarly, for , the solution is

(7) 
so the stable (normalized) Eigenvector is

(8) 
See also Anosov Map
© 19969 Eric W. Weisstein
19990525