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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: For each prime number , the dynamical behavior of the square mapping on the ring
of
-adic integers is studied. For
, there are only attracting fixed points with their attracting basins. For
, 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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Additional Information
Shilei Fan
Affiliation:
School of Mathematics and Statistics, Central China Normal University, 430079, Wuhan, People’s Republic of China
Email:
slfan@mail.ccnu.edu.cn
Lingmin Liao
Affiliation:
LAMA, UMR 8050, CNRS, Université Paris-Est Créteil Val de Marne, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France
Email:
lingmin.liao@u-pec.fr
DOI:
https://doi.org/10.1090/proc12777
Keywords:
$p$-adic dynamical system,
minimal decomposition,
square mapping
Received by editor(s):
August 23, 2014
Received by editor(s) in revised form:
March 7, 2015
Published electronically:
July 29, 2015
Additional Notes:
The first author was partially supported by self-determined research funds of CCNU (Grant No. CCNU14Z01002) and NSF of China (Grant No. 11231009). The second author was partially supported by 12R03191A - MUTADIS (France) and the project PHC Orchid of MAE and MESR of France.
Communicated by:
Yingfei Yi
Article copyright:
© Copyright 2015
American Mathematical Society