Dynamics of commuting rational maps on Berkovich projective space over ℂp

被引：0
|
作者：
Shi Lei Fan
Yue Fei Wang
机构：
[1] Chinese Academy of Sciences,Institute of Applied Mathematics, AMSS
[2] Chinese Academy of Sciences,Institute of Mathematics, AMSS
来源：
Acta Mathematica Sinica, English Series | 2013年 / 29卷
关键词：
Non-Archimedean field; Berkovich projective line; Fatou set; Julia set; 37P50; 37P40; 37P05;
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中图分类号：
学科分类号：
摘要：
We study the dynamics of commuting rational maps with coefficients in ℂp. By lifting the dynamics from ℙ1(ℂp) to Berkovich projective space ℙBerk1, we prove that two nonlinear commuting maps have the same Berkovich Julia set and the same canonical measure. As a consequence, two nonlinear commuting maps with coefficient in ℂp have the same classical Julia set. We also prove that they have the same pre-periodic Berkovich Fatou components.
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页码：1459 / 1478
页数：19
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