非阿局部域上幂级数的映射与动力性质  

Mapping and Dynamic Properties of Power Series over Non-archimedean Local Fields

作　　者：赵正俊 贾雪倩 Zheng Jun ZHAO;Xue Qian JIA(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,P.R.China)

机构地区：[1]安庆师范大学数理学院,安庆246133

出　　处：《数学学报（中文版）》2023年第3期539-546,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11971382);2022年安徽省高校学科(专业)拔尖人才学术资助项目。

摘　　要：设K是非阿局部域,D是K中的圆盘,Ф(z)=∑_(i=0)^(∞)c_(i)(z-a)^(i)∈K[[z-a]]是在D上收敛的非常值幂级数.利用非阿情形的最大模原理和growth增长模,给出了Φ是D上一一的若干充要条件.同时,利用所得结论讨论幂级数的相关动力性质.LetФ(z)=∑_(i=0)^(∞)c_(i)(z-a)^(i)∈K[[z-a]]be a non-constant power series which converges on a disk D in a non-archimedean local field K.In this paper,we present several necessary and suficient conditions for determining whether or not is one-to-one on D by the non-archimedean maximal modulus principle and growth modulus.Some dynamic properties of power series are discussed also in this paper.

关 键 词：幂级数 非阿域 周期点 算术动力性质 

分 类 号：O156.2[理学—数学]