Dynamics of commuting rational maps on Berkovich projective space over \(\mathbb C_p\)

DOI10.1007/s10114-013-2700-4zbMath1347.37161OpenAlexW2088725252MaRDI QIDQ2391995

Shilei Fan, Yue Fei Wang

Publication date: 6 August 2013

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-013-2700-4

zbMATH Keywords

Julia setFatou setnon-Archimedean fieldBerkovich projective line

Mathematics Subject Classification ID

Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Dynamical systems on Berkovich spaces (37P50) Non-Archimedean Fatou and Julia sets (37P40)

Cites Work

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• Brolin's equidistribution theorem in \(p\)-adic dynamics.
• The valuative tree
• Equidistribution of small points, rational dynamics, and potential theory
• Periodic points of rational functions in the \(p\)-adic hyperbolic space
• Invariant sets under iteration of rational functions
• Quantitative uniform distribution of points of small height on the projective line
• Valuative analysis of planar plurisubharmonic functions
• Closure of Periodic Points Over a Non-Archimedean Field
• A finiteness theorem for canonical heights attached to rational maps over function fields
• An invariant measure for rational maps
• Mesures et équidistribution sur les espaces de Berkovich
• Théorie ergodique des fractions rationnelles sur un corps ultramétrique

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