Non-integrability of ABC flow

被引：32

作者：

Maciejewski, A

Przybylska, M

机构：

[1] Univ Zielona Gora, Inst Astron, PL-65265 Zielona Gora, Poland

[2] Nicholas Copernicus Univ, Torun Ctr Astron, PL-87100 Torun, Poland

来源：

PHYSICS LETTERS A | 2002年 / 303卷 / 04期

关键词：

ABC flow; Ziglin theory; differential Galois theory; monodromy group; differential Galois group;

D O I：

10.1016/S0375-9601(02)01259-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate the ABC flow when A(2) = B-2, and we prove that this system does not admit a meromorphic first integral when ABC not equal 0. Moreover, for C-2/A(2) < 2 we prove that it does not possess a real meromorphic first integral. In our consideration we apply the Ziglin theory and the differential Galois theory. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：265 / 272

页数：8

共 28 条

[1]

[Anonymous], COMPUTER ALGEBRA DIF

[2]

ARNOLD V, 1965, CR HEBD ACAD SCI, V261, P17

[3]

Arnold V.I., 1984, SOME QUESTIONS MODER, P8

[4]

AUDIN M, 2001, SYSTEMES HAMILTONIEN

[5]

Balder A., 1996, FIELDS I COMMUN, V7, P5

[6]

BEUKERS F, 1989, NUMBER THEORY PHYSIC, P413

[7]

BOUCHER D, 2000, THESIS U LIMOGES FRA

[8] CHAOTIC STREAMLINES IN THE ABC FLOWS [J].

DOMBRE, T ;

FRISCH, U ;

GREENE, JM ;

HENON, M ;

MEHR, A ;

SOWARD, AM .

JOURNAL OF FLUID MECHANICS, 1986, 167 :353-391

[9]

GANTMAHER FR, 1988, THEORY MATRICES

[10]

HENON M, 1966, CR ACAD SCI A MATH, V262, P312

← 1 2 3 →