DYNAMICS OF THE SQUARE MAPPING ON THE RING OF p-ADIC INTEGERS

被引：8

作者：

Fan, Shilei ^{[1
]}

Liao, Lingmin ^{[2
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

[2] Univ Paris Est Creteil Val de Marne, CNRS, UMR 8050, LAMA, 61 Ave Gen Gaulle, F-94010 Creteil, France

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 03期

关键词：

p-adic dynamical system; minimal decomposition; square mapping; MINIMAL DECOMPOSITION; QUADRATIC MAPS; ERGODICITY; SYSTEMS; DIGRAPHS; VAN;

D O I：

10.1090/proc12777

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1183 / 1196

页数：14

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