The Theory of Linear Fractional Transformations of Rational Quadratics
نویسندگان
چکیده
A standard technique for solving the recursion xn+1 = g (xn) where g : C→ C is a complex function is to first find a fairly simple function g : C→ C and a bijection f : C→ C such that g = f◦g◦f−1 where ◦ is the composition of functions. Then xn = g (x0) = (f ◦ g ◦ f−1) (x0) where g and g are the n-fold composition of functions and g is fairly easy to compute. With this motivation we find all pairs of rational quadratic functions g, g such that for some
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A Theory of Linear Fractional Transformations of Rational Functions
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