PAINLEVE ANALYSIS FOR THE MIXMASTER UNIVERSE MODEL

被引:33
作者
CONTOPOULOS, G
GRAMMATICOS, B
RAMANI, A
机构
[1] UNIV PARIS 07, LPN, F-75251 PARIS, FRANCE
[2] UNIV FLORIDA, DEPT ASTRON, GAINESVILLE, FL 32611 USA
[3] ECOLE POLYTECH, CPT, CNRS, UPR 14, F-91128 PALAISEAU, FRANCE
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1993年 / 26卷 / 21期
关键词
D O I
10.1088/0305-4470/26/21/018
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We show that the mixmaster universe, or Bianchi IX, model passes the Painleve test in the form of the Ablowitz-Ramani-Segur algorithm, i.e. the solutions of the equations of motion do not have movable critical points. Thus this system is probably integrable and therefore non-chaotic.
引用
收藏
页码:5795 / 5799
页数:5
相关论文
共 25 条
[1]   A CONNECTION BETWEEN NON-LINEAR EVOLUTION-EQUATIONS AND ORDINARY DIFFERENTIAL-EQUATIONS OF P-TYPE .1. [J].
ABLOWITZ, MJ ;
RAMANI, A ;
SEGUR, H .
JOURNAL OF MATHEMATICAL PHYSICS, 1980, 21 (04) :715-721
[2]  
Arnowitt R., 1962, GRAVITATION INTRO CU, DOI DOI 10.1007/S10714-008-0661-1
[3]   OSCILLATORY APPROACH TO A SINGULAR POINT IN RELATIVISTIC COSMOLOGY [J].
BELINSKI.VA ;
KHALATNI.IM ;
LIFSHITZ, EM .
ADVANCES IN PHYSICS, 1970, 19 (80) :525-&
[4]  
BELINSKII VA, 1970, SOV PHYS JETP-USSR, V30, P1174
[5]  
BELINSKII VA, 1969, SOV PHYS JETP-USSR, V29, P911
[6]   NUMERICAL STUDY OF INITIALLY EXPANDING MIXMASTER UNIVERSES [J].
BERGER, BK .
CLASSICAL AND QUANTUM GRAVITY, 1990, 7 (02) :203-216
[7]   COMMENTS ON THE COMPUTATION OF LIAPUNOV EXPONENTS FOR THE MIXMASTER UNIVERSE [J].
BERGER, BK .
GENERAL RELATIVITY AND GRAVITATION, 1991, 23 (12) :1385-1402
[8]   INTEGRABLE HAMILTONIAN-SYSTEMS AND THE PAINLEVE PROPERTY [J].
BOUNTIS, T ;
SEGUR, H ;
VIVALDI, F .
PHYSICAL REVIEW A, 1982, 25 (03) :1257-1264
[9]   A NUMERICAL-ANALYSIS OF CHAOTIC BEHAVIOR IN BIANCHI IX MODELS [J].
BURD, AB ;
BURIC, N ;
ELLIS, GFR .
GENERAL RELATIVITY AND GRAVITATION, 1990, 22 (03) :349-363
[10]   CHAOTIC AND NONCHAOTIC BEHAVIOR IN THE MIXMASTER DYNAMICS [J].
FERRAZ, K ;
FRANCISCO, G ;
MATSAS, GEA .
PHYSICS LETTERS A, 1991, 156 (7-8) :407-409