Functional Equation
The functional equation arises in the study of one-dimensional maps that, as a function of a parameter, go through a period-doubling cascade. The functional equation is the mathematical expression of the universality of period doubling. The equation is used to specify a function g and a parameter λ by the relation
with the boundary conditions
- g(0) = 1,
- g′(0) = 0, and
- g′′(0) < 0
For a particular form of solution with a quadratic dependence of the solution near x=0, the inverse 1/λ=2.5029... is one of the Feigenbaum constants.
Read more about this topic: Feigenbaum Function
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