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$p$ -adic power series which commute under composition

Author(s): Hua-Chieh Li
Journal: Trans. Amer. Math. Soc. 349 (1997), 1437-1446.
MSC (1991): Primary 11S99; Secondary 11S31, 14L05
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Abstract: When two noninvertible series commute to each other, they have same set of roots of iterates. Most of the results of this paper will be concerned with the problem of which series commute with a given noninvertible series. Our main theorem is a generalization of Lubin's result about isogenies of formal groups.

References:

1.: N. Koblitz, -adic Numbers, -adic Analysis, and Zeta-Functions, Springer-Verlag, New York, 1977. MR 57:5964
2.: J. Lubin, Nonarchimedean Dynamical Systems, Comp. Math. 94 (1994), pp. 321-346. MR 96g:11140
3.: J. Lubin, One-parameter Formal Lie Groups over -adic Integer Rings, Ann. of Math. 80 (1964), pp. 464-484. MR 29:5827
4.: J. Lubin, Finite Subgroups and Isogenies of One-parameter Formal Lie Groups, Ann. of Math. 85 (1967), pp. 296-302. MR 35:189


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