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A survey on iterations in rings of formal power series in one indeterminate

Volume 125 / 2023

Wojciech Jabłoński Banach Center Publications 125 (2023), 45-70 MSC: Primary 13F25; Secondary 13J05, 39B52, 30D05, 13H05. DOI: 10.4064/bc125-5


The aim of the paper is to give a survey of results concerning iterations in rings of formal power series in one indeterminate. We characterize the algebraic structure of groups and maximal groups of commuting formal power series. We show also a detailed description of these groups. This allows us to give the form of all one-parameter groups of formal power series. As applications we give a solution of the embeddability problem in the ring of formal power series as well as we determine iterative roots of some formal power series.


  • Wojciech JabłońskiFaculty of Applied Mathematics
    AGH University of Science and Technology
    Mickiewicza 30, 30-059 Kraków, Poland

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