<i>p</i>-adic interpolation of iterates

Bjorn Poonen

Type: Article

Publication Date: 2014-03-18

Citations: 32

DOI: https://doi.org/10.1112/blms/bdu010

Abstract

Extending work of Bell and of Bell, Ghioca, and Tucker, we prove that for a p-adic analytic self-map f on a closed unit polydisk, if every coefficient of f ( x ) − x has valuation greater than that of p 1 / ( p − 1 ) , then the iterates of f can be p-adically interpolated; that is, there exists a function g ( x , n ) analytic in both x and n such that g ( x , n ) = f n ( x ) whenever n ∈ Z ⩾ 0 .

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