Closure of periodic points over a non-archimedean field

被引：55

作者：

Hsia, LC ^{[1
]}

机构：

[1] Natl Cent Univ, Dept Math, Chungli 32054, Taiwan

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2000年 / 62卷

关键词：

D O I：

10.1112/S0024610700001447

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：685 / 700

页数：16

共 16 条

[1]

[Anonymous], THESIS BROWN U

[2]

[Anonymous], 1981, GEOMETRIE ANAL RIGID

[3] GEOMETRY OF P-ADIC SIEGEL DISKS [J].

ARROWSMITH, DK ;

VIVALDI, F .

PHYSICA D-NONLINEAR PHENOMENA, 1994, 71 (1-2) :222-236

[4]

Beardon AF, 1991, GRADUATE TEXTS MATH, V132

[5] COMPLEX ANALYTIC DYNAMICS ON THE RIEMANN SPHERE [J].

BLANCHARD, P .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 11 (01) :85-141

[6]

Bosch S., 1984, Non-Archimedean analysis

[7]

Carleson L., 1993, COMPLEX DYNAMICS

[8]

Devaney R, 1987, An introduction to chaotic dynamical systems, DOI 10.2307/3619398

[9]

Hsia LC, 1996, COMPOS MATH, V100, P277

[10]

LUBIN J, 1994, COMPOS MATH, V94, P321

← 1 2 →