Dynamics of Commuting Rational Maps on Berkovich Projective Space over C_p  

作　　者：Shi Lei FAN Yue Fei WANG 

机构地区：[1]Institute of Applied Mathematics,AMSS,Chinese Academy of Sciences [2]Institute of Mathematics,AMSS,Chinese Academy of Sciences

出　　处：《Acta Mathematica Sinica,English Series》2013年第8期1459-1478,共20页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant Nos.10831008 and 11231009)

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 P1 Berk, 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.We study the dynamics of commuting rational maps with coefficients in Cp. By lifting the dynamics from P1（Cp） to Berkovich projective space P1 Berk, 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.

关 键 词：Non-Archimedean field Berkovich projective line Fatou set Julia set 

分 类 号：O157.5[理学—数学]