Suppose we have a function $F$ over a numeric pair (pair of real numbers) $[a, b]$ such that:

$$F([a,b]) = [1-br+a, 1-br+a+b]$$

find a function $G$ such that:

$$F = G(G([a,b]))$$

Is there a general algorithm to find such a function?

Suppose we have a function $F\colon \mathbb{R}^2 \to \mathbb{R}^2$ over a numeric pair (pair of real numbers) $[a, b]$ such that:

$$F([a,b]) = [1-br+a, 1-br+a+b]$$ for some $r\in\mathbb{R}$.

find a function $G\colon \mathbb{R}^2 \to \mathbb{R}^2$ such that, for each $[a,b]\in\mathbb{R}^2$:

$$F([a,b]) = G(G([a,b]))$$

Is there a general algorithm to find such a function?

Suppose we have a function F over a numeric pair (pair of real numbers) [a, b] such that:

$$F([a,b]) = [1-b*r+a, 1-b*r+a+b]$$

find a function G such that:

$$F = G(G([a,b]))$$

Is there a general algorithm to find such a function?

Suppose we have a function $F$ over a numeric pair (pair of real numbers) $[a, b]$ such that:

$$F([a,b]) = [1-br+a, 1-br+a+b]$$

find a function $G$ such that:

$$F = G(G([a,b]))$$

Is there a general algorithm to find such a function?

Suppose we have a function F over a numeric pair [a, b] such that:

$$F([a,b]) = [1-b*r+a, 1-b*r+a+b]$$

find a function G such that:

$$F = G(G([a,b]))$$

Is there a general algorithm to find such a function?

Suppose we have a function F over a numeric pair (pair of real numbers) [a, b] such that:

$$F([a,b]) = [1-b*r+a, 1-b*r+a+b]$$

find a function G such that:

$$F = G(G([a,b]))$$

Is there a general algorithm to find such a function?