p-adic interpolation of iterates
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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 [1over (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[superscript n](x) whenever n∈Z≥0.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Bulletin of the London Mathematical Society
Oxford University Press
Poonen, B. “p-Adic Interpolation of Iterates.” Bulletin of the London Mathematical Society 46, no. 3 (June 1, 2014): 525–527.