Power series in one variable

AbstractThis paper is concerned with the ring A of all complex formal power series and the group G of substitution-invertible formal series. The two main questions of interest will be these. How can one tell whether two members of A represent the same “function” up to “change of variables” by a member of G? Which members of G can be embedded in a one-parameter subgroup of G? Sections 1–4 give a self-contained account of the solution to these problems. This account is largely expository, most of the partial results having appeared elsewhere. Some of the proofs of the known results are new and simpler; some are just paraphrases. The sources of this material are given in a remark at the end of Section 4. Section 5 gives a new proof of the characterization of those one-parameter subgroups of G which consist wholly of convergent series