Abstract
The convergence of linear fractional transformations is an important topic in mathematics. We study the pointwise convergence of p-adic Möbius maps, and classify the possibilities of limits of pointwise convergent sequences of Möbius maps acting on the projective line ℙ1(ℂ p ), where ℂ p is the completion of the algebraic closure of ℚ p . We show that if the set of pointwise convergence of a sequence of p-adic Möbius maps contains at least three points, the sequence of p-adic Möbius maps either converges to a p-adic Möbius map on the projective line ℙ1(ℂ p ), or converges to a constant on the set of pointwise convergence with one unique exceptional point. This result generalizes the result of Piranian and Thron (1957) to the non-archimedean settings.
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Wang, Y., Yang, J. The pointwise convergence of p-adic Möbius maps. Sci. China Math. 57, 1–8 (2014). https://doi.org/10.1007/s11425-013-4750-6
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DOI: https://doi.org/10.1007/s11425-013-4750-6