Dynamics of commuting rational maps on Berkovich projective space over ℂ p |
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基金项目: | Supported by National Natural Science Foundation of China (Grant Nos.10831008 and 11231009) |
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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.
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关 键 词: | 地图 理性 Julia集 射影空间 非线性 CP 周期性 证明 |
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