非阿基米德動態系統與枝群

The action of the Galois groups on the roots of iterates of a noninvertible power series can be regarded as the automorphism groups of locally finite trees. In this project, we study both the branch groups and the Galois groups of the extension of the roots of iterates. From our study, we realize that the usual tree representation from the point of view of wreath product is too large for us to handle the iterated Galois groups. Branch groups on the other hand seem perfectly related to the action of the ramification groups on the roots of the iterated power series. We also include the results of my study about the ramification groups in this report.