On heights of $p$-adic dynamical systems
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Abstract:
When we consider the properties of the iterates of a noninvertible endomorphism of a formal group, all the roots of iterates of the endomorphism are simple and the full commuting family contains both invertible and noninvertible series. Experimental evidence seems to suggest that for an invertible series to commute with a noninvertible series with only simple roots of iterates, two such commuting power series must be endomorphisms of a single formal group. Lubin proposed four conjectures to support this conjecture. In this paper, we provide answers to these four conjectures.References
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Additional Information
- Hua-Chieh Li
- Affiliation: Department of Mathematics, National Tsing Hua University, Hsin Chu, Taiwan, Republic of China
- Address at time of publication: Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, Republic of China
- Email: li@math.nthu.edu.tw
- Received by editor(s): July 18, 2000
- Published electronically: July 25, 2001
- Communicated by: David E. Rohrlich
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 379-386
- MSC (2000): Primary 11S99; Secondary 11S31, 14S05
- DOI: https://doi.org/10.1090/S0002-9939-01-06166-4
- MathSciNet review: 1862116