## Arnold's Cat Map

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 non-Hamiltonian, nonanalytic, and mixing. However, it is Area-Preserving 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)