Painleve's analysis, integrability and detecting chaos-order-chaos transition by the SALI and mLE methods of three-dimensional Armbruster Guckenheimer Kim galactic potential

被引：4

作者：

Chatar, Walid ^{[1
]}

Kharbach, Jaouad ^{[1
]}

Benkhali, Mohamed ^{[1
]}

El Ghamari, Mohammed ^{[1
]}

Benmalek, Mohamed ^{[1
]}

Rezzouk, Abdellah ^{[1
]}

Ouazzani-Jamil, Mohammed ^{[2
]}

机构：

[1] Univ Sidi Mohamed Ben Abdellah, Fac Sci Dhar El Mahraz, Lab Phys Solide, BP 1796, Fez Atlas 30000, Morocco

[2] Univ Privee Fes, Lab Syst & Environm Durables, Lot Quaraouiyine Route Ain Chkef, Fes, Morocco

来源：

PHYSICS LETTERS A | 2021年 / 401卷

关键词：

Hamiltonian system; Painleve analysis; Three-dimensional integrability; Chaos-order-chaos transition; The Small Alignment Index (SALI) method; The maximum Lyapunov exponent (mLE);

D O I：

10.1016/j.physleta.2021.127331

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The three-dimensional (3D) Armbruster Guckenheimer Kim galactic potential in the general form is considered. The integrability of this problem is performed by using the Painleve analysis. We report three cases of integrability, and the exact integrals of motion are obtained explicitly for each case. Several numerical simulations were performed in order to investigate the classical phase space and explore chaos-order-chaos transition. Also, the maximum Lyapunov exponent (mLE) and the smaller alignment index (SALI) methods are used to distinguish rapidly and with certainty between ordered and chaotic motion. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：11