Lie's Data Transport Equation
Iterated functions crop up in the series expansion of the combined functions, such as g(f(x)). Given the iteration velocity, or beta function (physics), for the nth iterate of the function f, we have
For example, for rigid advection, if f(x) = x + a, then v(x) = a. Consequently g(x + a) = exp(a ∂/∂x) g(x), a plain shift operator.
Read more about this topic: Iterated Function
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