Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces

被引：9

作者：

Maciejewski, Andrzej J. ^{[1
]}

Szuminski, Wojciech ^{[2
]}

Przybylska, Maria ^{[2
]}

机构：

[1] Univ Zielona Gora, Janusz Gil Inst Astron, Licealna 9, PL-65407 Zielona Gora, Poland

[2] Univ Zielona Gora, Inst Phys, Licealna 9, PL-65407 Zielona Gora, Poland

来源：

PHYSICS LETTERS A | 2017年 / 381卷 / 07期

关键词：

Integrability obstructions; Liouville integrability; Morales-Ramis theory; Differential Galois theory; Constant curvature spaces; SPHERE;

D O I：

10.1016/j.physleta.2016.12.030

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We formulate the necessary conditions for the integrability of a certain family of Hamiltonian systems defined in the constant curvature two-dimensional spaces. Proposed form of potential can be considered as a counterpart of a homogeneous potential in flat spaces. Thanks to this property Hamilton equations admit, in a general case, a particular solution. Using this solution we derive necessary integrability conditions investigating differential Galois group of variational equations. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：725 / 732

页数：8

共 15 条

[1]

[Anonymous], 1969, Funkcial Ekvac

[2] A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane [J].

Ballesteros, Angel ;

Blasco, Alfonso ;

Herranz, Francisco J. ;

Musso, Fabio .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (34)

[3] The anisotropic oscillator on the 2D sphere and the hyperbolic plane [J].

Ballesteros, Angel ;

Herranz, Francisco J. ;

Musso, Fabio .

NONLINEARITY, 2013, 26 (04) :971-990

[4] Integrability of Hamiltonian systems with homogeneous potentials of degree zero [J].

Casale, Guy ;

Duval, Guillaume ;

Maciejewski, Andrzej J. ;

Przybylska, Maria .

PHYSICS LETTERS A, 2010, 374 (03) :448-452

[5] JORDAN OBSTRUCTION TO THE INTEGRABILITY OF HAMILTONIAN SYSTEMS WITH HOMOGENEOUS POTENTIALS [J].

Duval, Guillaume ;

Maciejewski, Andrzej J. .

ANNALES DE L INSTITUT FOURIER, 2009, 59 (07) :2839-2890

[6] Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry [J].

Herranz, FJ ;

Ortega, R ;

Santander, M .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (24) :4525-4551

[7] Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential [J].

Maciejewski, AJ ;

Przybylska, M .

JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (06)

[8] Non-integrability of Gross-Neveu systems [J].

Maciejewski, AJ ;

Przybylska, M ;

Stachowiak, T .

PHYSICA D-NONLINEAR PHENOMENA, 2005, 201 (3-4) :249-267

[9] Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces [J].

Maciejewski, Andrzej J. ;

Przybylska, Maria ;

Yoshida, Haruo .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (38)

[10]

Morales-Ruiz JJ., 2001, METHODS APPL ANAL, V8, P113, DOI DOI 10.4310/MAA.2001.V8.N1.A5

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