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

2014/08/20 by Shilei Fan, Fan, Shilei, Lingmin Liao +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.1408.4574

13 pages, 2 figures

arxiv created 2014/08/20 · arxiv updated 2014/08/21

Abstract

For each prime number p, the dynamical behavior of the square mapping on the ring ℤ_p of p-adic integers is studied. For p=2, there are only attracting fixed points with their attracting basins. For p≥ 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 1/p being attracting basins. All these minimal components are precisely exhibited for different primes p.

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