The best known example of an Anosov diffeomorphism. It is given by the transformation
(1)
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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)
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so
(3)
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The eigenvectors are found by plugging into the matrix equation
(4)
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For ,
the solution is
(5)
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where
is the golden ratio, so the unstable (normalized)
eigenvector is
(6)
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Similarly, for ,
the solution is
(7)
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so the stable (normalized) eigenvector is
(8)
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