Böttcher's equation
Böttcher's equation, named after Lucjan Böttcher, is the functional equation F ( h ( z ) ) = ( F ( z ) ) n {\displaystyle F(h(z))=(F(z))^{n}} where h is a given analytic function with a superattracting fixed point of order n at a, (that is, h ( z ) = a + c ( z − a ) n + O ( ( z − a ) n + 1 ) , {\displaystyle h(z)=a+c(z-a)^{n}+O((z-a)^{n+1})~,} in a neighbourhood of a), with n ≥ 2 F is a sought function. The logarithm of this functional equation amounts to Schröder's equation.