Some aspects of the local theory of generalized Dhombres functional equations in the complex domain
We study the generalized Dhombres functional equation (()) = (()) in the complex domain. The function is given and we are looking for solutions with (0) = and is a primitive root of unity of order ≥ 2. All formal solutions for this case are described in this work, for the situation where can be transformed into a function which is linearizable and local analytic in a neighbourhood of zero...