p-adic dynamic systems

被引：35

作者：

Albeverio, S ^{[1
]}

Khrennikov, A

Tirozzi, B

De Smedt, S

机构：

[1] Ruhr Univ Bochum, Inst Math, D-44780 Bochum, Germany

[2] Essen Bochum Dusseldorf, Dusseldorf, Germany

[3] BiBoS Res Ctr, D-33615 Bielefeld, Germany

[4] CERFIM, Locarno, Switzerland

[5] Univ Vaxjo, Dept Math, S-35195 Vaxjo, Sweden

[6] Univ Roma La Sapienza, Dipartimento Fis, I-00185 Rome, Italy

[7] Free Univ Brussels, Fac Toegepaste Wetenschappen, B-1050 Brussels, Belgium

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 1998年 / 114卷 / 03期

关键词：

Prime Number; Periodic Point; Siegel Disk; Cyclic Attractor; Invariant Sphere;

D O I：

10.1007/BF02575441

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Dynamic systems in non-Archimedean number fields (i.e., fields with non-Archimedean valuations) are studied. Results are obtained for the fields of p-adic numbers and complex p-adic numbers. Simple p-adic dynamic systems have a very rich structure-attractors, Siegel disks, cycles, and a new structure called a "fuzzy cycle." The prime number p plays the role of a parameter of the p-adic dynamic system. Changing p radically changes the behavior of the system: attractors may become the centers of Siegel disks, and vice versa, and cycles of different lengths may appear or disappear.

引用

页码：276 / 287

页数：12

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