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In dynamical systems theory, the horseshoe map
was introduced by Stephen Smale as a simple model of complex behavior. It
is given on the unit square by the formula:
- (1) (xn + 1,yn + 1) =
H((xn,yn)),
where:
- (2)
This map serves as a model for general behavior at transverse homoclinic points, and can be fairly easily shown to have an invariant compact set on which it acts as a shift map.
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