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Closure of Periodic Points Over a Non‐Archimedean Field
Author(s) -
Hsia LiangChung
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001447
Subject(s) - closure (psychology) , field (mathematics) , mathematics , set (abstract data type) , periodic point , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , computer science , market economy , programming language , economics
The closure of the periodic points of rational maps over a non‐archimedean field is studied. An analogue of Montel's theorem over non‐archimedean fields is first proved. Then, it is shown that the (nonempty) Julia set of a rational map over a non‐archimedean field is contained in the closure of the periodic points.