Permutable Power Series and Regular Iteration

convergent for \z\ < p, where p > 0, then f(z) is said to have a fixpoint of multiplier ax at 2 = 0. In the (local) iteration of/(?) one studies the sequence {/„(*)},» = 0, 1, 2, • • • in a neighbourhood of z — 0, /n(z) being defined by /oto = * . / « « = / 0 i t o } ^r » = 1 , 2 , 3 , . . . For many values of the multiplier ax, including 0 < \ax\ < 1 and \ax\ > 1, the local iteration of f(z) is completely mastered by the introduction of Schroder's functional equation