CURRENT TRENDS AND OPEN PROBLEMS IN ARITHMETIC DYNAMICS

被引：37
作者：
Benedetto, Robert [1 ]
Ingram, Patrick [2 ]
Jones, Rafe [3 ]
Manes, Michelle [4 ]
Silverman, Joseph H. [5 ]
Tucker, Thomas J. [6 ]
机构：
[1] Amherst Coll, Dept Math & Stat, Amherst, MA 01002 USA
[2] York Univ, Dept Math & Stat, N520 Ross,4700 Keele St, Toronto, ON M3J 1P3, Canada
[3] Carleton Coll, Dept Math & Stat, Northfield, MN 55057 USA
[4] Univ Hawaii, Dept Math, 2565 McCarthy Mall, Honolulu, HI 96822 USA
[5] Brown Univ, Math Dept, Box 1917, Providence, RI 02912 USA
[6] Univ Rochester, Math Dept, 915 Hylan Bldg, Rochester, NY 14627 USA
来源：
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 56卷 / 04期
关键词：
Arithmetic dynamics; open problems; MORDELL-LANG CONJECTURE; FINITE-FIELD PERMUTE; P-ADIC DYNAMICS; PERIODIC POINTS; QUADRATIC POLYNOMIALS; PREPERIODIC POINTS; WANDERING DOMAINS; RATIONAL MAPS; DEGREE-GROWTH; PRIMITIVE DIVISORS;
D O I：
10.1090/bull/1665
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry and partly from p-adic analogues of theorems and conjectures in classical complex dynamics. In this article we survey some of the motivating problems and some of the recent progress in the field of arithmetic dynamics.
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收藏
页码：611 / 685
页数：75
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