## Nonarchimedean dynamical systems and formal groups

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## Abstract:

We prove two theorems that confirm an observation of Lubin concerning families of $p$-adic power series that commute under composition: under certain conditions, there is a formal group such that the power series in the family are either endomorphisms of this group or semiconjugate to endomorphisms of this group.## References

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## Additional Information

**Laurent Berger**- Affiliation: UMPA de l’ENS de Lyon, UMR 5669 du CNRS, 69007 Lyon, France
- Email: laurent.berger@ens-lyon.fr
- Received by editor(s): November 27, 2017
- Received by editor(s) in revised form: December 18, 2017, September 3, 2018, and September 5, 2018
- Published electronically: January 9, 2019
- Communicated by: Romyar T. Sharifi
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 1413-1419 - MSC (2010): Primary 11S82; Secondary 11S31, 32P05
- DOI: https://doi.org/10.1090/proc/14401
- MathSciNet review: 3910408