Dynamics of the square mapping on the ring of 𝑝-adic integers

Fan, Shilei; Liao, Lingmin

doi:10.1090/proc12777

Dynamics of the square mapping on the ring of -adic integers

Authors: Shilei Fan and Lingmin Liao
Journal: Proc. Amer. Math. Soc. 144 (2016), 1183-1196
MSC (2010): Primary 37P05; Secondary 11S82, 37B05
DOI: https://doi.org/10.1090/proc12777
Published electronically: July 29, 2015
MathSciNet review: 3447671
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Abstract: For each prime number , the dynamical behavior of the square mapping on the ring $\mathbb{Z}_p$ of -adic integers is studied. For , there are only attracting fixed points with their attracting basins. For $p\geq 3$ , there are a fixed point 0 with its attracting basin, finitely many periodic points around which there are countably many minimal components and some balls of radius being attracting basins. All these minimal components are precisely exhibited for different primes .

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