Arnold's cat map
Chaotic map from the torus into itself
Arnold's cat map
In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name. It is a simple and pedagogical example for hyperbolic toral automorphisms. Thinking of the torus T 2 {\displaystyle \mathbb {T} ^{2}} as the quotient space R 2 / Z 2 {\displaystyle \mathbb {R} ^{2}/\mathbb {Z} ^{2}} , Arnold's cat map is the transformation Γ : T 2 → T...
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