A maximally superintegrable system on an n-dimensional space of nonconstant curvature

被引：44

作者：

Ballesteros, A. ^{[3
]}

Enciso, A. ^{[4
]}

Herranz, F. J. ^{[3
]}

Ragnisco, O. ^{[1
,2
]}

机构：

[1] Univ Roma 3, Dipartimento Fis, Via Vasca Navale 84, I-00146 Rome, Italy

[2] Inst Nazl Fis Nucl, I-00146 Rome, Italy

[3] Inst Nazl Fis Nucl, Dept Fis, I-00146 Rome, Italy

[4] Univ Complutense, Dept Fis Teor 1, E-28040 Madrid, Spain

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2008年 / 237卷 / 04期

关键词：

superintegrable systems; variable curvature; coalgebra symmetry;

D O I：

10.1016/j.physd.2007.09.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a novel Hamiltonian system in n dimensions which admits the maximal number 2n - 1 of functionally independent, quadratic first integrals. This system turns out to be the first example of a maximally superintegrable Hamiltonian on an n-dimensional Riemannian space of nonconstant curvature, and it can be interpreted as the intrinsic Smorodinsky-Winternitz system on such a space. Moreover, we provide three different complete sets of integrals in involution and solve the equations of motion in closed form. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：505 / 509

页数：5

共 38 条

[1] The Toda lattice is super-integrable [J].

Agrotis, MA ;

Damianou, PA ;

Sophocleous, C .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2006, 365 (01) :235-243

[2]

[Anonymous], NICHTEUKLIDISCHE GEO

[3]

Arnol'd V.I., 1997, MATH ASPECTS CLASSIC

[4] Maximal superintegrability on N-dimensional curved spaces [J].

Ballesteros, A ;

Herranz, FJ ;

Santander, M ;

Sanz-Gil, T .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (07) :L93-L99

[5] CLASSICAL AND QUANTUM INTEGRABLE SYSTEMS: THE COALGEBRA APPROACH [J].

Ballesteros, A. ;

Musso, F. ;

Ragnisco, O. .

REGULAR & CHAOTIC DYNAMICS, 2002, 7 (04) :393-398

[6] A systematic construction of completely integrable Hamiltonians from coalgebras [J].

Ballesteros, A ;

Ragnisco, O .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1998, 31 (16) :3791-3813

[7] Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature [J].

Ballesteros, Angel ;

Herranz, Francisco J. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2007, 40 (02) :F51-F59

[8]

Bertrand J., 1873, CR HEBD ACAD SCI, V77, P849

[9] A geometrical approach to the problem of integrability of Hamiltonian systems by separation of variables [J].

Bruce, AT ;

McLenaghan, RG ;

Smirnov, RG .

JOURNAL OF GEOMETRY AND PHYSICS, 2001, 39 (04) :301-322

[10] Two new classes of isochronous Hamiltonian systems [J].

Calogero, F .

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2004, 11 (02) :208-222

← 1 2 3 4 →